The increasing development and use of digital health interventions requires good quality costing information to inform development and commissioning choices about resource allocation decisions. The Narrative Experiences Online (NEON) Intervention is a web-application that delivers recorded mental health recovery narratives to its users. Two randomized controlled trials are testing the NEON Intervention in people with experience of psychosis (NEON) and people experiencing non-psychosis mental health problems (NEON-O).This study describes and estimates the cost components and total cost of developing and delivering the NEON Intervention.Total costs for the NEON Trial (739 participants) and NEON-O Trial  were estimated by: identifying resource use categories involved in intervention development and delivery; accurate measurement or estimation of resource use; and a valuation of resource use to generate overall costs, using relevant unit costs. Resource use categories were identified through consultation with literature, costing reporting standards and iterative consultation with health researchers involved in NEON Intervention development and delivery. Sensitivity analysis was used to test assumptions made.The total cost of developing the NEON Intervention was £182,851. The largest cost components were software development (27%); Lived Experience Advisory Panel workshops (23%); coding the narratives (9%); and researchers' time to source narratives (9%). The total cost of NEON Intervention delivery during the NEON Trial was £118,663 (£349 per NEON Intervention user). In the NEON-O Trial, the total delivery cost of the NEON Intervention was £123,444 (£241 per NEON Intervention user). The largest cost components include updating the narrative collection (50%); advertising (19%); administration (14%); and software maintenance (11%). Uncertainty in the cost of administration had the largest effect on delivery cost estimates.Our work shows that developing and delivering a digital health intervention requires expertise and time commitment from a range of personnel. Teams developing digital narrative interventions need to allocate substantial resources to curating narrative collections.This study identifies the development and delivery resource use categories of a digital health intervention to promote the consistent reporting of costs and informs future decision-making about the costs of delivering the NEON Intervention at scale.http://www.isrctn.com/ISRCTN11152837. NEON-O Trial: ISRCTN63197153, registered 9 January 2020, http://www.isrctn.com/ISRCTN63197153.NEON Trial: ISRCTN11152837, registered 13 August 2018,  In recent years, there has been a rapid increase in digital health technologies (DHTs) to deliver mental health interventions remotely, either to replace or supplement face-to-face healthcare, with that increase accelerating during the COVID-19 pandemic .Digital health technologies range from predefined functions such as remote diagnosis or disease monitoring, to more complex functions around supporting behavior change through interactive and personalized interactions. A sub-type of DHTs are digital health interventions (DHIs), which provide users with remote access to treatment through text messaging services, smartphone apps, and web-based resources. Recent reviews of the growing number of trials have shown promising but varied effectiveness for DHIs in a wide range of mental health conditions, including but not limited to depression , 4, eatiInvestment in mental health DHIs is increasing, partly to improve access to care in overstretched health systems and partly due to emerging patient and user preference for DHI delivery of mental health care . This meThere is a lack of standardization in how costs are reported and described for economic evaluations of DHIs , 15. TheDevelopment costs are not typically considered in economic evaluations as, by definition, they have already been incurred prior to delivery. Historically, these development costs are sunk costs, and may include cross-subsidization of product development where there is a failure to reach product launch. Development costs can be included in a market price, which will fall as the market share, or the number of users increases. A recent systematic review reported development costs were only reported in four out of 24 economic evaluations of internet-based interventions for anxiety and depression . There aThe aim of this study is to describe, estimate, and present the associated cost components and total cost of developing and delivering the Narrative Experiences Online (NEON) Intervention, using current recommendations for costing DHIs , 21, 22.The NEON Intervention is a web-based application that delivers recorded recovery narratives to its users. A systematic review  and qualThe NEON Intervention was then developed . The NEOn = 739) and people experiencing non-psychosis mental health problems   to evaluate the cost-effectiveness of offering the NEON Intervention to individuals with experience of psychosis  , 41.This study reports the estimation of development and delivery costs for the NEON Intervention, which is used in both trials.This study was conducted as part of the Narrative Experiences Online (NEON) Programme (researchintorecovery.com/neon), which is investigating whether receiving recorded mental health recovery narratives improves the quality of life in people who experience mental health issues.Estimated total cost and individual cost components for the development and delivery of the NEON Intervention are reported. The development costs included those incurred from the perspective of the research body who funded the development and testing of the NEON Intervention. The delivery costs included those incurred from the perspective of the health and social care provider  . The lenThe development costs begin from the start of the current research program funding, comprising software and intervention development, through feasibility testing and up to the starting point of the definitive trial. Early conceptual development work, and research-related tasks including the randomized controlled trials which contribute to a large part of the program grant, are excluded in the development cost estimates. The duration of the development of the NEON Intervention was considered over the period January 2017 to January 2021.The total cost for the development stage of the NEON Intervention was constructed with reference to a development costing checklist for a digital program for training community health workers to deliver treatment for depression . The cosThe product of resource use and unit costs generated total cost estimates, and this is referred to as the base-case analysis. In this study, the resource use data obtained for development and delivery was obtained for the whole user cohort (top-down costs), rather than data relevant to a specific user (bottom-up costs). Therefore, the approach taken was to generate total development and delivery costs and then apportion to individual users as a “mean cost per user.” The number of users was defined as the number of people randomized to the intervention group .In the base-case analysis, costs for human resources were obtained by multiplying the personnel's midpoint hourly salary plus on-costs (pension contributions and payroll taxes) by the proportion of hours spent on the task. For external experts and consultants their costs were recorded as invoices to the NEON study. In some cases where records were not kept, the proportion of hours spent on a task was estimated through expert consultation to produce the maximum and minimum plausible duration; with the midpoint (average) selected during the base-case analysis. For information technologies used in the development and delivery of the NEON Intervention, financial records were used to calculate the cost of the components purchased. In one case, an estimate was derived from the NEON budget proposal.Deriving estimates of certain cost components required some assumptions to be made with uncertainty further associated with the true values of several components. To assess the impact of our assumptions and parameter uncertainty, all input parameters were adjusted to their extreme values individually in a one-way sensitivity analysis. Tornado diagrams  were useThis costing study was developed and reported in accordance to standard validation and reporting criteria . A team We identified several resource use categories in intervention development and delivery, summarized in Four components that incurred resources were needed to develop the NEON Intervention:building a collection of recovery narratives (the NEON Collection) that would be used in the intervention  workshops to develop recommendations on (1) the ethical issues around narrative curation and (2) the initial curation procedures, Collection Steering Group (CSG) meetings to make decisions on (1) the inclusion of individual narratives and (2) refinement of the curation procedures, training researchers to use the INCRESE tool, coding narratives using INCRESE);developing the web-application as a platform to deliver the NEON Intervention ;additional communications necessary to develop the intervention ;n = 25; follow-up: n = 22) with experience of mental health problems);testing the intervention . This group was comprised of four LEAP members, a senior research fellow, and a research assistant. In total, there were eight meetings lasting 2 h per session with preparation for the meetings completed by an administrator; referred to as an Administrator, Professional, Managerial level 3 (APM3) within the host university. All the CSG meetings were necessary for the development of the NEON Intervention.A CSG had the authority to make all final ethical decisions regarding the approval of narratives into the collection where the research team expressed uncertainty surrounding whether all inclusion criteria were met and/or whether an exclusion criterion was met. Moreover, the steering group could make recommended updates to the inclusion and exclusion criteria  are spread between both graphic design and software development costs. Interaction design was also important to ensure the web-application's functions operated as intended .Throughout the NEON study, task meetings were used to communicate and raise general discussions surrounding the interventions development. An assumption was made, through inspection of meeting agendas, that 33% of task meetings were necessary for the purpose of developing the intervention . A total of 86 meetings were held with recorded attendance from members of the NEON team.The international advisory board was used to provide expert consultation on safety strategies for the development of the NEON Collection and to provide advice on intervention engagement strategies. The meeting was attended by four professors and members of the NEON study team. During the intervention development stage, there was a single Intervention Design group meeting aimed at discussing particular features of the intervention and how they could be improved. This meeting was attended by two LEAP members and a senior research fellow. As before, all meetings had expenses covered.To ensure that the evolving intervention operated as intended, the web-applications functions were tested by researchers using dummy accounts as well as data collection tools. This included testing of forms used to collect demographics and outcome data, and interactive features included to provide access to recovery narratives. During the analysis, the full intervention testing costs were deemed necessary for the development of the NEON Intervention on the basis that monitoring routine outcomes and usage data, necessary for the NEON trials, is commonplace in clinical practice .Finally, a feasibility study to evaluate a prototype delivery of the NEON Intervention in a population of people with experience of mental health problems was conducted . The usehttps://aws.amazon.com/lightsail/). This service allows websites to host a specific number of users for a publicly advertised price. The current intervention is designed to host 2,000 users. Therefore, a specific level of resource use was predetermined. The invoices from the supplier were made over a monthly billing period in US Dollars (USD); the exchange rates were determined by the credit card issuer.The web hosting capacity of the site, together with associated cyber-security features, is supplied by Amazon Web Services Lightsail . The number of days spent training the administrator was recorded for each personnel conducting the training see . TraininThe NEON Intervention required new narratives to be introduced into the collection over time to maintain diversity and relevance to users. Firstly, we consulted with the NEON team to estimate that an additional 200 narratives per year would be needed based on preliminary work looking at the diversity of the current NEON Collection. The cost per narrative was calculated from the current collection size of 659 recovery stories then re-scaled to 200 narratives. Although the cost per narrative approach can provide an estimate of the cost to update the narrative collection, it explicitly assumes a linear relationship between the cost and the narrative collection size. There is uncertainty about whether the cost of updating the narrative collection will increase or decrease for newly sourced narratives. In reality, the process of updating the narratives may become more streamlined and productivity gains can be made in coding the narratives. On the other hand, the cost of updating the narrative collection may be greater if sourcing new narratives becomes more cumbersome, e.g., exhausting the number of existing collections to source narratives.The web-application requires ongoing maintenance to ensure the NEON Intervention can be delivered as intended for its users. There are challenges in costing for web-application maintenance due to the variability in need for maintenance and the broad definition of what maintenance means in practice. In this case, we define web-application maintenance as any change, modification, or update to the web-application codebase to correct faults, to improve performance, or to update the content on the web-application.To deliver the NEON Intervention, it was assumed that 9.75 h per week of administrative support by an APM2 is required to conduct operational tasks . The hours per week was estimated by assuming a smaller proportion (50%) of the administrative support observed during the NEON trials (19.5 h per week) would be required in a routine operational setting.Operational activities that may have influenced the NEON Intervention's effectiveness  were also considered to be a delivery cost. Advertisement for the study following agreed advertising principles  to recruThroughout the delivery of the NEON Intervention, the NEON study was responsible for the wellbeing of those using the NEON Intervention. Safeguarding concerns were dealt with during the trials by the clinical principal investigator.To assess the impact of our assumptions and parameter uncertainty, all input parameters were varied to their extreme values in one-way sensitivity analysis. To examine the impact of the structural assumptions, scenario analysis was used. The assumptions that were made during the base-case analysis for both the development and delivery of the NEON Intervention and the sensitivity and scenario analyses are shown in In the base-case, the total number of hours to develop the intervention  was 2,709 h (45.2 days). The resource items that required the most personnel time were the staff time to code the narrative collection ; the staff time to source recovery narratives (562 h); task meetings (341 h); and LEAP workshops (328 h). The members of staff that contributed the most hours include the coding researchers , the research assistants (895 h), and the senior research fellows (394 h). The cost per unit of staff time varied from £18.25 to £69.91 per hour.A summary of the estimated costs of developing the NEON Intervention is provided in In the base-case, the total number of personnel hours to deliver the intervention during the NEON trial was 1,708 h (28.5 days). In the NEON-O trial, the total number of personnel hours to deliver the intervention was 1,776 h (29.6 days). The resource items that require the most personnel time were the administrative support (54%); maintenance (19%); advertising (17%). The cost per unit of resource use varied between £2.40 and £125.A summary of NEON Intervention delivery costs is provided in The one-way sensitivity analysis of the most sensitive cost components for NEON Intervention development are presented as a Tornado diagram in The one-way sensitivity analysis of the cost components for the NEON Intervention delivery during the NEON trial are presented as a Tornado diagram in The scenario analysis of the structural assumptions for developing the NEON Intervention are presented as a Tornado diagram in The scenario analysis of the structural assumptions for the NEON Intervention delivery during the NEON trial are presented in As expected, increasing the number of users, reduced the cost per user year, such that 500, 1,000, or 2,000 users cost £137.04, £68.52, £34.26, respectively.We identified several resource use categories for intervention development and delivery through a literature review and work with experts on the research team. Developing the NEON Intervention cost £182,851, which was largely attributed to building the NEON Collection  and developing the web-application . The curation costs were mostly made up of LEAP meetings (50%); narrative coding using the INCRESE tool (20%); and the researchers' time to source recovery narratives (19%). The largest components of the web-application costs included software development (77%); developing the recommender system (12%); and the graphic design costs (7%).Delivering the NEON Intervention during the NEON trial and NEON-O trial costed £118,663 and £123,444, respectively. This equates to £349  and £241  per user. Over an annual period, the NEON Intervention cost was £68,521. Delivery costs were driven by updating the narrative collection (50%); advertisement (19%); and administrative support. Similarly to other studies , we founThe strength of our study is the use of published guidelines where available to inform our costing methods. We have provided detailed and transparent reporting of cost components and we have utilized multi-disciplinary input into identifying categories, including strong service user involvement. We have carried out sensitivity analysis to make explicit which parameters are associated with uncertainty, and the direction and magnitude of that uncertainty.The limitations of our study include the necessary use of expert opinion sources where primary data were not collected or available. Due to limitations in patient-level resource use data availability, we have had to use top-down costing methods rather than bottom-up, or micro-costing approaches, which arguably does not provide a patient-level cost sensitive to different levels of usage by individual patients. This limitation is common to costing DHIs, due to the nature of the costs involved .Defining a starting point for development costs necessarily meant excluding early development costs. As with other research-led endeavors, this work is supported by the accumulation of an existing knowledge base and the experience and expertise of the research team, as well as the opportunity cost of the researchers. This can be conceptualized using the health service research payback model which examines the complex interaction and costs of early and late publicly-funded research, and their effect on research outputs . There hThe delivery costs provided here are derived from the delivery of the NEON Intervention during the trials, so it is likely that delivery costs in practice will be different, and health care payers need to be prepared for costs to vary once the intervention is implemented outside a clinical trial environment. How the NEON Intervention is implemented in the NHS will likely determine what resources will be needed in future versions of the intervention. As the NEON trials do not compare the NEON Intervention with a face-to-face version of the same intervention, we are not able to examine the differences in costs (or effectiveness) between these two scenarios.Assumptions had to be made around tasks and roles taken up by researchers in the trial that would actually be covered by healthcare professionals, administrators, and other members of the healthcare team when the intervention is delivered in practice. Necessarily there are likely to be some differences between trial delivery and practice delivery. For example, the clinical principal investigator coordinated all safeguarding activities during NEON Intervention delivery as part of the RCT. If the NEON Intervention is rolled out in practice, at a substantial scale, then the safeguarding approaches and infrastructure needed will necessarily be different. Safeguarding approaches will need to scale with safeguarding demands, and to take into account different regulatory requirements in everyday practice compared to clinical trials. We have treated advertising costs in the trials as a proxy for accessing patients in practice. Recruitment for the NEON Trial was targeted carefully, for example through the production of several 100 online messages with content specific to a psychosis trial and the design and dissemination of targeted adverts . This involved human effort and expertise to design these materials. If the NEON Intervention is rolled out to a general mental health population on a larger scale through online mechanisms, then less targeting of recruitment material might be needed, and individual messages or adverts can also be reused and redeployed. This means that the human cost of generating recruitment material might be less and the dominant cost might be spent on the services that social media companies provide to promote messages to a relevant audience. Especially at the point where the NEON Intervention is deployed on a wider scale, the cost of recruiting one person through social media promotion should be routine to estimate.via primary care or the voluntary sector, to “direct to consumer” (costs associated with advertising), and the value for money offered by these different implementation routes (which may be separate or additive) that could be evaluated in relation to reach and engagement. The most efficient way to implement DHIs like the NEON Intervention is very relevant in a resource-constrained system as implementation methods cost money and affect the effectiveness and cost-effectiveness of the DHI , through to the implementation  the DHI .Other limitations in the delivery costs include the lack of regulatory or scale-up costs, such that these costs may be an underestimate of true costs once the NEON Intervention is implemented in practice. The derivation of costs per user from top-down costs necessarily means that the cost per user is related to the number of users assumed in the calculations. The number of users could be the number of people in each trial, the number of people eligible to use the NEON Intervention in the real world , or we wGiven the evolving nature of DHIs, input parameters into economic evaluations (like delivery costs) need to be re-examined at different stages of the intervention capacity. It is likely that certain cost components will change over time. Hosting costs are likely to reduce due to increases in process performance and reductions in storage cost per unit (Moore's Law) , and salAnother issue beyond the scope of this study is the likelihood that the intervention will be delivered differently once it is implemented in practice. This will have an impact not only on resource use but also on effectiveness of the intervention. However, the data we have provided will provide healthcare providers with approximations of the resources required to deliver the intervention in practice.We are not aware of a DHI that has focused on the use of narratives to support recovery in mental health, so it is not possible to compare our development and delivery costs with another equivalent intervention or directly relevant costing study. It is also unclear as to the utility of comparing the costs we have estimated with other mental health DHIs costs, due to the lack of comparability of costing methods between studies. The reporting of different development and delivery cost components of mental health DHIs varies, making meaningful comparison difficult , 15.Development costs are reported in a minority of economic evaluations, as they are usually seen as sunk costs and not relevant to the health and social care provider. The list price of commercially developed healthcare products such as pharmaceuticals are perceived to include development costs and thus recoup those costs. Development costs are more difficult to determine for DHIs. Opinions differ on the inclusion of development costs, and it is the perspective that should determine whether they are included or not . When deWhen reported, development costs vary from as little as £19,000  to £500,In a recent review of methods used in economic evaluations of mental health DHIs, 16 out of 66 did not report staffing costs as part of delivery costs . Given tWe used the NICE guidance to support our costing methodology. However, there have been questions raised surrounding how fit for purpose this guidance is for costing DHIs in practice . Like otHuman resources constituted a large proportion of our development and delivery costs. These estimates were affected by uncertainties around which costs to include, other than salary, so we followed the PSSRU approach to include employers' costs, as well as estates and indirect costs for the organization employing that person . Our senThis study makes two knowledge contributions. First, it provides a usable estimate of the cost of developing and implementing a DHI from software and intervention development, through feasibility testing and up to commencement of the definitive trial. This can be used to inform commissioning of new DHIs in general, giving explicit consideration to all the different types of resources required, and the quantity and cost, as well as specifically, the implementation of the NEON Intervention. Second, the costing challenges which have been identified indicate the need for updated best practice guidance for economic evaluation of DHIs by NICE and other clinical and funding agencies.The NEON Intervention is intended for widespread use as a low-cost self-management intervention. Two uses are envisaged: adjunctive to clinical treatment and direct access. This study identifies the costs associated with population-level roll-out of the NEON Intervention. In relation to use within services, the staff costs needed to support access are identified. In relation to direct access, the public health costs associated with maintaining and developing the intervention are estimated. We are currently evaluating the effectiveness of the NEON intervention based on the two RCTs described in this study. Data analysis is near completion and will be published separately building on the findings in this study. These findings will inform decision-making about whether, and how, to implement the NEON Intervention at scale.The original contributions presented in the study are included in the article/The studies involving human participants were reviewed and approved by Leicester Central Research Ethics Committee, 19/EM/0326. Informed consent to participate was obtained from all participants using an online form. The patients/participants provided their written informed consent to participate in this study.RE, SG, LP, and SR-E contributed to the conception and design of the study. LP carried out the data collection and analysis and wrote the first draft of the manuscript. SR-E, SG, and RE wrote sections of the manuscript. JL-B, FN, CB, AG, JN, DQ, and SB contributed to the data collection. JL-B and FN provided feedback on the analysis. MS is the chief investigator for this trial. RE is the lead health economist. All authors have read, commented, and reviewed the manuscript.This study was funded by the NIHR [Personal experience as a recovery resource in psychosis: Narrative Experiences Online (NEON) Programme (RP-PG-0615-20016)]. The funder was not involved in the development of the methods, data collection, analysis or writing of this manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care.


Image segmentation is a critical step in digital image processing applications. One of the most preferred methods for image segmentation is multilevel thresholding, in which a set of threshold values is determined to divide an image into different classes. However, the computational complexity increases when the required thresholds are high. Therefore, this paper introduces a modified Coronavirus Optimization algorithm for image segmentation. In the proposed algorithm, the chaotic map concept is added to the initialization step of the naive algorithm to increase the diversity of solutions. A hybrid of the two commonly used methods, Otsu’s and Kapur’s entropy, is applied to form a new fitness function to determine the optimum threshold values. The proposed algorithm is evaluated using two different datasets, including six benchmarks and six satellite images. Various evaluation metrics are used to measure the quality of the segmented images using the proposed algorithm, such as mean square error, peak signal-to-noise ratio, Structural Similarity Index, Feature Similarity Index, and Normalized Correlation Coefficient. Additionally, the best fitness values are calculated to demonstrate the proposed method's ability to find the optimum solution. The obtained results are compared to eleven powerful and recent metaheuristics and prove the superiority of the proposed algorithm in the image segmentation problem. Digital image processing is manipulating digital images through algorithms using digital computers for many purposes, such as image enhancement, image compression, and extracting useful information . Image sMultilevel thresholding is more appropriate in images containing many objects with fine details and complex backgrounds because bi-level thresholding fails to distinguish these objects correctly. After all, it divides the image into only two regions . On the Over the last few years, Swarm intelligence has been extensively applied to solve multilevel thresholding image segmentation problems . Many alSeveral algorithms have been proposed in medical images, such as ant colony optimization with Cauchy and greedy levy mutations for COVID X-ray images segmentation . BandyopIn recent years, chaotic maps were incorporated into the swarm intelligence algorithms to increase the diversity of solutions and avoid falling into local optimum . HongweiCoronavirus Optimization Algorithm (COVIDOA) is a recent metaheuristic inspired by the replication lifecycle of Coronavirus . COVIDOAThis paper introduces the chaotic map concept into the novel Coronavirus Disease Optimization Algorithm (COVIDOA) to increase the diversity of solutions. The proposed algorithm is applied to solve the multilevel thresholding image segmentation problem of satellite images and a set of benchmark images. The proposed algorithm used a hybrid fitness function to find the optimum threshold values by adding weights to the Otsu and Kapur methods. The results showed that using the hybrid fitness function and adding the chaotic maps yields significantly better results than the other proposed algorithms. The motivation for using modified COVIDOA for satellite image segmentation is as follows: The No Free Lunch (NFL)  theorem Additionally, the basic and the binary versions of COVIDOA have performed much better in solving many benchmark and real-world problems , 42; reaThe chaotic logistic map is used to initialize COVIDOA to increase the diversity of solutions.A new hybrid fitness function is used for finding the optimum thresholds by assigning weights to the Otsu and Kapur methods.The superiority of the proposed algorithm is validated by applying it to six satellite and six benchmark images.The proposed method for image segmentation results is compared with many state-of-the-art algorithms focusing on the recently proposed metaheuristics.Several measures are used to evaluate the performance of the proposed algorithm in solving multilevel thresholding problems, such as best fitness value, MSE, PSNR, SSIM, FSIM, and NCC, and conducting the Wilcoxon rank-sum test to prove the efficiency of the proposed algorithm.The main contributions of this paper can be summarized as follows:This paper is organized as follows: Sect. t is based on the pixel intensity of the image, where pixels whose intensity values below t are assigned to region 1, and the other pixels are assigned to region 2  as follows:Virus mutationX is the solution before mutation, Z is the mutated solution, Xi and Zi are the ith element in the old and new solutions, respectively, i =1, …, D, and r is a random value in the range . MR is the mutation rate.Coronavirus uses the mutation technique to resist the human immune system . In the New virion releaseThe newly created virus particle leaves the infected cell targeting new healthy cells. In the proposed algorithm, if the fitness of the new solution is better than the parent solution fitness, the parent solution is replaced by the new one. Otherwise, the parent solution remains. The pseudocode of the COVID algorithm is as follows:COVIDOA is a recent evolutionary optimization algorithm inspired by the replication mechanism of Coronavirus when getting inside the human body . The repIn COVIDOA, each virus particle represents a solution in the population. The dimension of each solution is equal to the number of threshold values needed for segmentation plus 1. The first population solution is initialized randomly, where each element in the solution vector is assigned a value within the range of pixel intensities of the grayscale image. For the remaining solutions in the population, the initialization is done using chaotic maps to generate a uniformly distributed initial population , 45. We Sine Chaotic map:Singer Chaotic Map:Sinusoidal Chaotic Map:Chebyshev Chaotic Map:Tent Chaotic Map:Logistic Chaotic Map:Iterative Chaotic Map:Gauss/Mouse Chaotic Map:In the chaotic initialization, given the solution vector Chaotic initialization is a modern technique used to ensure that the solutions of the initial population are uniformly distributed, which helps avoid the problem of getting stuck into local minima or maxima . As discIn this section, we firstly provide a brief description of the datasets used for testing. Then, we show the parameter settings for the proposed and state-of-the-art algorithms. After that, the evaluation metrics used for comparing the results are explained in detail. Finally, we present the numerical results of running the proposed algorithm and its peers.Six satellite images are selected from “NASA Visible Earth”  to proveThey have proved their superior performance in optimization problems, especially image segmentation.Most of them are recent and published in reputable sources.https://www.mathworks.com/).Their MATLAB implementations are publicly available on the MATLAB website  , ReptileThe parameters of all algorithms are set as mentioned in their original papers. In all algorithms, the population size is 50, and the maximum number of iterations to 100. All algorithms were run 20 times, and the best-obtained results are reported in the results section.The performance of the proposed algorithm is evaluated using several performance metrics, including Mean Square Error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), Feature Similarity Index (FSIM), Normalized Correlation Coefficient (NCC), and best fitness in addition to the Wilcoxon rank-sum test.Best fitnessThe maximum fitness is obtained from running the proposed ad state-of-the-art algorithms with the proposed hybrid fitness function equations . By triaMean Square Error (MSE)MSE is commonly used to estimate the error between the original and segmented images. It can be calculated as follows:F is the original image, f is the segmented image, and Peak signal-to-noise ratio (PSNR)PSNR is commonly used to quantify the quality of images. It refers to the ratio between the segmented image power and noise powerStructural similarity index (SSIM)F and f are the original and segmented images. F and f, respectively. F and f, respectively. C1 = 6.502 and C2 = 58.522.SSIM is used to quantify the structural similarity between the original and segmented images as follows:Feature similarity index (FSIM)PC is the phase congruence, and FSIM is used to measure the similarity in the structure of the two images as follows:Normalized correlation coefficient (NCC)F and f is calculated as follows:NCC is used to measure the extent to which two images are related. The absolute value of NCC ranges from 0 to 1, where 0 indicates that the two images have no relation and 1 indicates the strongest possible relation. The higher the absolute value of NCC, the stronger the relationship between the two images. NCC between the original and segmented images Wilcoxon rank-sum testThe Wilcoxon rank-sum test is a nonparametric statistical test used to measure the statistical difference between two related methods . We condPSNR, SSIM, and NCC are used to measure the quality of the segmented images, while best fitness is measured to prove the ability of the proposed algorithm to find optimum solutions, and the Wilcoxon rank-sum test is utilized to prove the statistical significance of the proposed algorithm as follows:This section presents the numerical results of running the proposed algorithm to select the optimum threshold values using the proposed hybrid fitness function with chaotic initialization. These results are compared with the state-of-the-art algorithms in best fitness, MSE, PSNR, SSIM, FSIM, NCC, and Wilcoxon rank-sum test. The experiments have been performed using 6, 10, 14, 18, 22, and 26 thresholds.Firstly, a comparison between the results of the various chaotic maps is conducted to demonstrate that the logistic map gives the best results among the others, as shown in Table The higher PSNR, SSIM, FSIM, NCC, and fitness values and lower MSE values resulting from the chaotic logistic map demonstrate its robustness. Hence, the chaotic logistic map is utilized while performing further experiments.Table All algorithms have been applied to solve multilevel thresholding problems for both the standard and satellite images to show the effectiveness of the proposed algorithm against other proposed methods. The results for the six benchmark images are shown in Tables These experiments proved the ability of the proposed algorithm to find the threshold values that most fit segmentation. In terms of the best fitness, it is noticed from Tables The MSE values in Tables Regarding PSNR, the proposed algorithm outperforms the other algorithms in 28 from 36 cases for the benchmark images and 30 from 36 cases for the satellite images. Also, the SSIM and FSIM metrics are measured to evaluate the similarity between the original and segmented images. The SSIM results of all algorithms are shown in Tables According to FSIM, the proposed algorithm is superior in 30 and 29 of 36 cases for the benchmark and satellite images, respectively, as shown in Tables Finally, the NCC is evaluated to measure the correlation between the original and segmented images. According to the NCC results shown in Tables The proposed algorithm is compared to its peers in terms of the total average values for fitness, MSE, PSNR, SSIM, FSIM, and NCC, and the results are shown in Fig. As shown in Fig. The segmented images produced by the proposed algorithm at different thresholds are shown in Figs. Additionally, some convergence curves are displayed in Fig. Due to the random process in optimization algorithms, the results differ at each run. The results of 5 separate runs of the proposed algorithm for segmentation of Image1 and Sat_img1 are shown in Table P values produced by the Wilcoxon rank-sum test must be ≤ 0.05 to be good evidence against the null hypothesis.In addition to the previously mentioned evaluation criteria, the Wilcoxon rank-sum test is utilized to prove the statistical significance of the proposed algorithm. This test compares two methods based on the null hypothesis, which assumes no significant difference between the two methods. The P values produced by comparing the proposed algorithm with all other algorithms are shown in Tables P values shown in the table are ≤ 0.05, which proves the alternative hypothesis that assumes a significant difference between the two methods. The overall results prove the efficiency of the proposed algorithm in image segmentation.The Satellite image segmentation aims to get a map composed of a few categories  from a multispectral satellite image in many applications such as geoscience studies, astronomy, and geographical information systems. This paper proposes an improved Coronavirus Disease Optimization algorithm for solving satellite image's multi-level thresholding segmentation problem. The concept of chaotic initialization is embedded into the proposed algorithm to improve the searchability of the initial population and to void the problem of getting stuck into local minima or maxima. Additionally, a hybrid fitness function is utilized to measure the fitness of solutions instead of the classic Otsu and Kapur methods. Two separate datasets are segmented using the proposed algorithm, and several evaluation criteria have been utilized to measure the performance. The experimental results proved that the proposed algorithm with chaotic initialization and the hybrid fitness function results in image segmentation with better performance than other metaheuristics. Future work will apply the proposed algorithm to image segmentation of color images.


Due to the influence of nonlinear loads, power quality control devices under the traditional double closed-loop control strategy suffer from a large output voltage harmonic distortion rate and a slow harmonic suppression response and cannot meet the high-quality power supply requirements of high-end manufacturing. A compound control strategy based on voltage feedback and current feed-forward is proposed to solve the voltage quality problem under a nonlinear load. Firstly, based on the mathematical model of power quality control device, the working principle and voltage current coupling relationship are analyzed. Then, an output voltage compound control strategy based on feed-forward and feedback is proposed, and the harmonic suppression mechanisms are deduced and analyzed. Finally, simulation and experimental results are presented to show that, compared with the traditional double closed-loop control strategy, the harmonic suppression effect of the composite control strategy proposed in this paper can be increased by 2.2%, and the response time is decreased to 100 ms. With the upgrading of China’s manufacturing industry, a number of high-tech industries represented by precision processing, chip and electronic manufacturing, data centers and so on have developed rapidly. Considering that the high-precision production equipment in these high-tech industries are very sensitive to voltage sag, three-phase imbalance and harmonic voltage ,2, the pBased on modern power electronics technology and modern control theory, the cascaded power quality improvement device ,7 has beAffected by nonlinear loads, unbalanced loads, semiconductor devices, line impedance and other factors, the voltage at the common connection point (PCC) on the output side of the cascaded power quality improvement device will be distorted . TherefoConsidering that the traditional double closed loop control algorithm is difficult to improve the voltage harmonics at the common connection point, a composite control strategy based on voltage feedback and current feed-forward is proposed. By detecting the PCC point voltage for harmonic voltage feedback control and detecting the PCC point current for harmonic current feed-forward control, the compound control strategy can not only improve the output voltage harmonic compensation effect but can also ensure the output voltage harmonic compensation speed, so as to be suitable for suppressing voltage harmonic distortion caused by the rapid change of hybrid load. In order to verify the effectiveness of the proposed composite control strategy, a simulation and experimental verification were carried out through the simulation model and test platform and it was proven that the composite control strategy based on feed-forward and feedback can effectively improve the harmonic distortion rate. The contribution of this paper is listed as follows:1. A novel composite control strategy based on voltage feedback and current feed-forward is proposed, which can compensate not only stable nonlinear loads but also rapidly changing nonlinear loads;2. The harmonic suppression mechanism and realization method of voltage feedback and current feed-forward in the proposed compound control strategy are studied in depth;3. The proposed composite control strategy is simulated and tested, and the compensation effect and dynamic response performance of the control strategy are verified.The topological structure of the cascaded power quality improvement device is shown in In au, bu, cu represent the output voltages of the device, ai, bi, ci represent the output currents of the device, pau, pbu, pcu represent the three-phase voltages of the PCC, and Lai, Lbi, Lci represent the load currents.R represents the sum of the power switch tube loss resistance and the line loss resistance; fL and fC are the resistance values of the three-phase filter inductor and filter capacitor; and L represents the sum of the line inductance on the output side of the device and the leakage inductance of the transformer.According to the circuit topology shown in Three-phase time-varying ac is not conducive to the design of the control system. This paper uses coordinate transformation to obtain a mathematical model based on d and q coordinates and convert the fundamental sine variables into DC variables. After converting the time-varying AC quantity to the DC quantity, the difficulty of the control system design can be reduced and the static error-free control can be realized. After the expression (1) is transformed by Park, the following expression can be obtained :(2){ud= coordinate system, the value of the 5th harmonic in the coordinate system can be calculated. The calculation process is shown in expression (5). The subscript N5 in Formula (5) represents five negative sequence transformations.The 5th harmonic voltage is converted into a negative sequence, and the d-axis rotates clockwise at an angular velocity of 5In the expression (5), set the 5th harmonic command value to 0. After the control system is stabilized, the 5th harmonic voltage will tend to 0. Obviously, the given value of the system controller is relatively simple, and it is easy to implement without considering the initial phase angle, frequency and other issues.In addition, when the 5th harmonic does not exist in the linear load, expression (5) is equal to zero. For the linear load, the 5th harmonic voltage feedback control loop will not play a role, so the control algorithm can run stably when the load is linear. The principle of elimination of the 7th harmonic is the same, except that the 7th harmonic uses the 7th positive sequence transformation.When nonlinear loads such as diodes and rectifiers are connected to the back end of the device, the harmonic current generated by the nonlinear load will form harmonic voltage on the line impedance. The virtual impedance can reshape the output impedance of the device at each harmonic frequency, thereby effectively solving the problem of voltage harmonics generated by nonlinear loads.This paper adopts a current feed-forward control strategy based on virtual impedance. First, the dq component (including interference) of each harmonic current is obtained by rotating transformation, and the interference is filtered through a low-pass filter (LPF), and then each harmonic current component is obtained. Finally, each harmonic of the voltage is compensated separately. Among them, the harmonic impedance of each order can be obtained by the corresponding harmonic current empirical formulas (6) and (7) .The positive sequence virtual impedance as:The negative sequence virtual impedance as:When the voltage drop of virtual harmonic inductor and virtual harmonic resistor cancel each other with the harmonic voltage drop of each harmonic current on the line impedance, the harmonic suppression function can be realized. The overall control block diagram is shown in GB/T 24337-2009 standard stipulates that the total harmonic distortion rate of public distribution network must be ≤4%. In order to verify the effectiveness of the proposed control algorithm, the system simulation model and experimental platform as shown in In Comparing In order to make a clearer comparison of compensation effect of the feedback and feed-forward composite control strategy, the voltage harmonic content before and after compensation were extracted in this paper, which is shown in In The comparison of response time and suppression effect under three different harmonic control strategies is shown in In order to verify the tracking and response ability of the proposed control strategy under nonlinear load dynamic changes, it was verified by simulation in this paper, and the results are shown in In In order to verify the composite control strategy and simulation test results in this paper, an experimental platform was built according to The experimental platform controller was the digital signal processor TMS320F28069 and the experimental waveforms were recorded by Fluke Oscilloscope 190–204. A novel composite control strategy based on voltage feedback and current feed-forward was proposed in this paper, which can solve the problem of high voltage harmonic content at the common connection point of the power quality control device. The simulation and experimental results verified the effectiveness of the compound control strategy. The proposed compound control strategy had the following characteristics:1. The current feed-forward control in the compound control strategy can reduce the harmonic impedance of the device at each frequency by introducing virtual harmonic impedance, so it can effectively reduce the voltage distortion rate at the common connection point;2. The proposed composite control strategy can reduce the harmonic voltage content of the common connection point from 6.8% to 1.8%, and the response time was only 100 ms. It met the stringent requirements of the high-end manufacturing industry for high voltage harmonic compensation accuracy and fast response time;3. Based on the harmonic suppression effect tested and analyzed on the 380 V low-voltage test platform, we believe the control strategy proposed in this paper is also applicable to the cascaded power quality control device at the 10 kV voltage level.


Coordinated positioning based on direction of arrival (DOA)–time difference of arrival (TDOA) is a research area of great interest in beyond-visual-range target positioning with shortwave. The DOA estimation accuracy greatly affects the accuracy of coordinated positioning. With existing positioning methods, the elevation angle’s estimation accuracy in multipath propagation decreases sharply. Accordingly, the positioning accuracy also decreases. In this paper, the elevation angle is modeled as a random variable, with its probability distribution reflecting the characteristics of multipath propagation. A new coordinated positioning method based on DOA–TDOA and Bayesian estimation with shortwave anti-multipath is proposed. First, a convolutional neural network is used to learn the three-dimensional spatial spectrogram to make an intelligent decision on the number of single and multiple paths, and to obtain a probability distribution of the elevation angle under multiple paths. Second, the elevation angle’s estimated value is modified using the elevation angle’s probability distribution. The modified elevation angle’s estimated value is substituted into a DOA pseudo-linear observation equation, and the target position’s estimated value is obtained using the matrix QR decomposition iteration algorithm. Finally, a TDOA pseudo-linear observation equation is established using the target estimate obtained in the DOA stage, and the coordinated positioning result is obtained using the matrix QR decomposition iteration algorithm again. Simulation results demonstrated that the proposed method had a stronger anti-multipath capability than traditional methods, and it improved the coordinated positioning accuracy of the DOA and TDOA. Measured data were used to validate the proposed method. Shortwave communication is an important means of long-distance communication and it has the characteristics of high destructibility and strong mobility. Shortwave signal source positioning has wide applications in both the military and civilian fields ,2. TargeFor propagation within the visual range, researchers have proposed many algorithms for DOA positioning ,5,6, TDOThe multipath effect under the ionospheric influence leads to difficulties in shortwave positioning, which has a great impact on the estimation of positioning parameters such as the arrival angle, and thus, the positioning accuracy. In actual shortwave positioning, the measurement error of the azimuth angle can reach about 3°, while the measurement error of the elevation angle can reach about 5–10°. Therefore, the elevation angle is not usually used for positioning. At present, data fusion is used to handle multipath data after the signal is received in the main methods designed for multipath scenarios ,19,20. HTo summarize, in this paper, shortwave anti-multipath coordinated positioning with DOA–TDOA is addressed. To accurately reflect the characteristics of ionospheric reflection, the arrival elevation angle was simulated as a random variable with a Gaussian mixture model (GMM). First, a convolutional neural network (CNN) was used to learn the three-dimensional spatial spectrogram to identify the modes of single-path propagation and multipath propagation. The corresponding probability distribution of the elevation angle was obtained and used to modify the estimated value of the elevation angle. Then, a two-dimensional DOA pseudo-linear observation equation was established based on the azimuth estimate and the elevation angle’s modified estimate. The matrix QR decomposition iteration algorithm proposed in  was usedThe remainder of this paper is as follows: The ionospheric signal channel varies randomly with space, time, and frequency, which has an impact on transmitted signals such as multipath fading and polarization fading. The electromagnetic wave incident in the ionosphere is divided into an ordinary (O) mode and unusual (X) mode. These two modes correspond to different paths and generate multipath fading. Ionospheric passive oblique detection technology can be used to obtain the ionospheric information regarding the reflection points between the transmitting and receiving stations. The high frequency radio signal is transmitted by the transmitting station, and the delay in the propagation time is calculated by the signal received by the receiving station, so as to infer the characteristics of the ionosphere. Multipath propagation in the spatial spectrogram is manifested by multiple spectral peaks at the same azimuth. Therefore, angle estimation ambiguity may occur . Figure Remark 1.Only one single path and two paths are taken as examples to illustrate the influence of multipath on the spatial spectrogram. When the number of paths increases, the spectral peak of spatial spectrum will increase correspondingly; however, the case for a larger number of paths is very rare .When the fading amplitude follows the Rayleigh distribution, the probability distribution of the multipath time delay follows a normal distribution . Inspirep elements, there are q signals that have incident angles ith signal, respectively. The arrival azimuth refers to the angle between the incident direction of the signal and the north direction of the local observation station. The elevation angle refers to the angle between the incident direction of the signal and the surface plane of the observation station. The output of the kth element in the antenna array can be expressed asith incident signal in the array, ith signal array, For an assumed circular array with It is assumed that the array elements are isotropic and there are no impacts, such as channel inconsistency and mutual coupling. Therefore, In Equation (2), Remark 2.is the array manifold matrix, which is related to the shape of the array and the direction of the signal. In practice, the shape of the antenna array will not change once it is fixed, sois closely related to the direction of the signal. In practice, the self-adjustment of the antenna array can ensurecan be used for angle estimation, and there will be no ill-conditioned matrix.  stands for additive noise. The larger it is, the lower the accuracy of angle estimation. When it reaches a certain level, angle estimation cannot be carried out. In addition, does not have a substantial impact on the structure of matrixandonly has an impact on the estimation accuracy.Under the narrowband model defined in Equation (2), the DOA estimation based on the multiple signal classification (MUSIC) algorithm is given byIn Equation (3), (1)Calculate the covariance matrix of array output data based on Equation (2);(2)Eigenvalue decomposition is performed on the covariance matrix obtained in step (1) to obtain the signal subspace (3)Search the angle corresponding to the maximum value of Equation (3), which is the angle estimate value.The MUSIC algorithm is a classical direction of arrival estimation algorithm, and the main steps are as follows:N DOA positioning observation stations and M TDOA positioning observation stations, which are denoted as The positioning scenario in this study is the same as that in , with N The positioning algorithm is divided into two stages. In the first stage, the pseudo-linear observation equations of the azimuth and the elevation angle are established, as shown in Equation (4). According to the geographical constraints of the earth surface and the algebraic relationship between the auxiliary variables lgorithm  as folloith observation station, respectively.In the second stage, the pseudo-linear equation of the time difference is established based on the DOA estimate, as shown in Equation (7). Similarly, Equations (5) and (7) are combined to construct an estimation criterion that contains the double quadratic equality. The matrix QR decomposition iteration algorithm is used to obtain the final positioning results .(7)Bτu| (73) of . R0 is tThe CNN is a type of feedforward neural network that contains convolutional computation and a deep structure ,23. It iIn this study, the CNN was used to detect and identify spatial spectrograms to discriminate between a single path and multiple paths. In the multipath case, the CNN was used to obtain the elevation angle of each path.The problem of path number discrimination based on spatial spectrograms belongs to an image classification problem with supervised learning. In this study, 10,000 spatial spectrogram images with different numbers of paths were generated with an elevation angle range of 5° to 70°. The number ratio between the single path and the two paths was approximately 1:1. The spatial spectrogram contained RGB images of 256 × 256 pixels.Remark 3.When there are multiple signals, there are many possible combinations of signals and the number of paths, which will lead to the very complex training process of neural network and a large amount of training data is required. In addition, based on the theory of array signal processing , when thRemark 4.The network used in this paper can be used to identify the number of paths under more paths, and only needs to increase the corresponding training data. However, the case for a larger number of paths is very rare  so this The CNN structure is shown in The loss curves of the training set and validation set are shown in After the number of paths was determined, the search for the spectral peak in the spatial spectrogram was performed using a regression method based on the CNN. The regression network model structure is shown in A simulation was conducted to generate 10,000 spatial spectrogram images that included a single path and two paths for a specific region. The elevation angles of the two paths followed a GMM. First, the number of paths was determined by the path discrimination model to obtain the numbers of single-path and two-path spectrograms, which were 3823 and 6177, respectively. For the single-path spatial spectrograms, the elevation angle was obtained using a traditional search method for the spectral peak. For the two-path spatial spectrums, the network shown in r is the location of the measurement station and t is time. Different from traditional methods in which the elevation angle is considered as a deterministic parameter for direction measurement, in this paper, Bayesian estimation theory was introduced and the elevation angle distribution under the ionospheric multilayer reflection was considered as prior information to estimate the maximum posterior probability of the elevation angle as follows:Under the influence of multipath fading, the elevation angle The prior distribution information of the elevation angle can be used to modify the posterior probability to obtain the modified posterior probability. This idea is important and provided by Equation (9). According to this idea, the prior distribution of the elevation angle can be used to modify the elevation angle’s estimated value obtained using Equation (3).It should be noted that the elevation angle’s correction only involved multiplying the angle’s estimate by a coefficient, so that the increase in the computational effort was limited. Although the prior probability distribution of the elevation angle requires a large amount of data analysis, the computation is an offline process. Therefore, only one deep learning calculation is needed to obtain the distributions for actual positioning.ith DOA observation station is as follows:R is the average radius of the earth, and ith observation station, respectively, in the earth-centered earth-fixed coordinate system.As shown in The modified estimates of the azimuth and the elevation angle were obtained using Equation (3) and (11). The estimates were substituted into Equation (4) to obtain the pseudo-linear equations of the azimuth and the elevation angle. The matrix QR decomposition iteration algorithm was used to obtain the DOA stage positioning results.According to mth observation station and the arrival time at the first observation station can be calculated asTherefore, the difference between the arrival time of the signal at the Considering K denotes the number of Monte Carlo simulation runs. K takes 5000 in the simulation.Simulations were conducted to verify the positioning performance of the proposed method. The default settings of the simulation parameters included the following. The longitude and latitude of the radiation source were 134° and 34°, respectively. There were seven shortwave observation stations, among which the first three had the DOA positioning system and the last four had the TDOA positioning system. Their longitudes, latitudes, and corresponding ionospheric reflection heights are shown in The ionospheric multipath reflection model and its variation trends with respect to time were validated using measured data. The transmitting station used in the experiment was a radio station in Urumqi , Xinjiang, China. The receiving station was a 20-channel shortwave direction measurement array located in Zhengzhou , Henan Province, China. The experimental parameters are shown in In this paper, DOA–TODA coordinated positioning for shortwave radiation sources was addressed based on prior information regarding the distribution of the elevation angles. First, a CNN was used to determine the number of single and multiple paths. The probability distribution of the elevation angle with the corresponding number of paths was learned. Then, the DOA and TDOA observation models were constructed according to the ionospheric virtual reflection model. The elevation angle’s estimated value was modified using the elevation angle’s prior information. An optimization model with double quadratic equality constraints was constructed according to the pseudo-linear equations of the azimuth, the elevation angle, and TDOA. The matrix QR decomposition iteration algorithm was used to solve the model.Simulations were conducted for the single-path and two-path cases. The simulation results demonstrated that compared with traditional methods, the proposed method achieved better positioning accuracy when the angle error was large, and anti-noise performance improved with strong anti-multipath performance. Moreover, the proposed method generalized the target position. Finally, the measured data were used to validate the proposed method. It should be noted that in this paper, only DOA–TDOA coordinated positioning for stationary targets was addressed. A future study needs to be conducted for moving targets.


Lung cancer is a leading cause of cancer-related deaths globally. Early detection is crucial for improving patient survival rates. Deep learning (DL) has shown promise in the medical field, but its accuracy must be evaluated, particularly in the context of lung cancer classification. In this study, we conducted uncertainty analysis on various frequently used DL architectures, including Baresnet, to assess the uncertainties in the classification results. This study focuses on the use of deep learning for the classification of lung cancer, which is a critical aspect of improving patient survival rates. The study evaluates the accuracy of various deep learning architectures, including Baresnet, and incorporates uncertainty quantification to assess the level of uncertainty in the classification results. The study presents a novel automatic tumor classification system for lung cancer based on CT images, which achieves a classification accuracy of 97.19% with an uncertainty quantification. The results demonstrate the potential of deep learning in lung cancer classification and highlight the importance of uncertainty quantification in improving the accuracy of classification results. This study’s novelty lies in the incorporation of uncertainty quantification in deep learning for lung cancer classification, which can lead to more reliable and accurate diagnoses in clinical settings. Lung cancer is a devastating disease that often has a grim prognosis. An early identification and diagnosis are vital to improving the chances of survival. One cutting-edge diagnostic tool for lung cancer is CT scan imaging. Deep learning (DL) has recently emerged as a powerful tool for processing medical images and has demonstrated great promise in detecting pulmonary nodules. However, the prediction accuracy of neural networks (NNs) in DL is uncertain, as the inner workings of their hidden layers are often considered a “black box,” making their predictions difficult to interpret . MachineIn the field of medical imaging, deep learning techniques such as convolutional neural networks (CNNs) and deep neural networks (DNNs) are widely used . While CIncorporating uncertainty into DL models can enhance their reliability and efficiency and help medical experts make more informed decisions. For instance, in diagnosing lung cancer, UQ can be used to identify areas in the images that require a further examination and avoid incorrect predictions. This is particularly crucial, as incorrect predictions can result in delayed treatment and decreased survival rates. Moreover, UQ can also be utilized to develop more robust and generalizable DL models that can adapt to new and unseen data. This is particularly important in the medical field, where there are often limited labeled datasets and new data types are constantly emerging .In conclusion, uncertainty quantification in DL for medical imaging plays a crucial role in ensuring the reliability and efficiency of DL models and can lead to more informed decisions for medical experts.Using uncertainty quantification in deep learning models can be crucial in the medical field, especially in diagnosing lung cancer. By incorporating uncertainty into these models, they can provide medical experts with a probabilistic interpretation of the predictions, which can help them understand the reasoning behind the model’s output. Bayesian deep learning methods, such as Bayesian neural networks (BNNs) and Monte Carlo dropout, have been shown to perform well in uncertainty quantification and provide more accurate and reliable results. These methods allow the model to randomly drop out neurons during the inference process, generating multiple predictions and helping to estimate the uncertainty in the model’s output. Incorporating uncertainty into deep learning models for medical imaging applications is crucial for improving the accuracy and reliability of the predictions. The use of Bayesian deep learning methods can provide medical experts with a better understanding of the reasoning behind the model’s output and help them make more informed decisions. Further research in this area can lead to the development of more robust and generalizable deep-learning models, which can significantly improve the accuracy of medical diagnoses.Incorporating both aleatoric and epistemic uncertainty into the classification model can help improve the predictions’ reliability. The proposed method in this study considers both types of uncertainty by incorporating MC dropout into the classification model to estimate epistemic uncertainty and by using a Bayesian NN to estimate aleatoric uncertainty. The results of this study demonstrate the importance of considering uncertainty in medical imaging classification tasks as it can lead to the improved accuracy and reliability of the model’s predictions. It is important to note that the proposed method is only a starting point for further research in medical imaging classification and uncertainty quantification. There is still much work to be done to fully understand the impact of uncertainty on the predictions of deep learning models and to develop more robust and effective methods for incorporating uncertainty into these models. Nevertheless, this study highlights the potential of incorporating uncertainty into medical imaging classification tasks and the importance of continued research in this area.Aleatoric uncertainty refers to the inherent uncertainty in the data, such as measurement errors or other sources of randomness. Epistemic uncertainty, on the other hand, refers to the uncertainty that arises from the model’s lack of knowledge about the genuine underlying relationship between the inputs and outputs. In medical imaging, aleatoric uncertainty could arise from measurement errors in the CT scan. In contrast, epistemic uncertainty arises due to the lack of knowledge or information about the data. These uncertainties can affect the accuracy and reliability of the predictions made by a model. In medical imaging applications, it is essential to consider and quantify both types of uncertainty to ensure the reliability and robustness of the model’s predictions. In In the context of lung cancer CT scans, aleatoric uncertainty can be caused by several factors, such as measurement errors during imaging, variability in the tissue density, or the limited sample sizes of CT scans. Epistemic uncertainty can result from a lack of information about the scans or the classification model. For example, suppose the model used for automated tumor classification is trained on various CT scans. In that case, it may not perform well on scans with different imaging characteristics, leading to higher epistemic uncertainty. A lack of understanding of the mechanisms contributing to tumor development can lead to a higher epistemic uncertainty. Baresnet aims to minimize both forms of uncertainty to increase the accuracy and reliability of lung cancer tumor classification. By merging ResNet with three standard models, we aim to incorporate stochastic and knowledge-based uncertainty to create more robust predictions. Minimizing uncertainty can provide medical professionals with more precise and reliable forecasts, leading to a better diagnosis and treatment decisions for lung cancer.The purpose of this research is to address the lack of trust in the prediction of current data mining and image processing procedures for lung cancer detection. By introducing Baresnet, the researchers aim to achieve a state-of-the-art performance in tumor classification, improve the precision of the classification, and control feature selection using Grad-CAM. The proposed model achieved an accuracy of 97.19%, a precision of 91.68%, a sensitivity of 98.82%, a specificity of 92.56%, and an F1 score of 97.47% for lung cancer classification.Development of a novel method for automated lung cancer detection using CT scans: this work proposes a new approach for detecting lung cancer in CT scans that utilizes deep learning and computer vision techniques.Utilization of deep neural networks trained with Grad-CAM: the proposed approach utilizes deep neural networks trained with the Grad-CAM method, which helps to highlight the regions of the CT scan that contribute the most to the predictions made by the model.Achieving a state-of-the-art performance in tumor classification: the proposed approach has been shown to achieve a state-of-the-art performance in terms of the accuracy and precision in tumor classification, outperforming the existing methods in the field.Improving the precision and control over the feature selection with Grad-CAM: by utilizing the Grad-CAM method, this work also improves the precision of the classification and provides a mechanism for controlling feature selection in the model, which is essential for ensuring the robustness of the results.The key contributions of this work can be summarized as follows:The main difference between our paper and the state of the art.The text discusses the importance of uncertainty quantification (UQ) in deep learning (DL) for medical imaging. DL techniques, such as CNNs and DNNs, are widely used in medical imaging, but their hidden layers are often considered a “black box,” making their predictions difficult to interpret. Incorporating a UQ can improve the reliability and efficiency of DL models, allowing medical experts to make more informed decisions. Bayesian neural networks (BNNs) and Monte Carlo (MC) are effective methods for UQ in DL. By considering uncertainty, DL models can be adapted to new and unseen data, making them more robust and generalizable.Diverse DL methods have dominated the world of medical image processing. Be-yond automatic radiological functions , ML has been applied to various “data enhancement” problems. Data processing or optimization seeks to improve accuracy, primarily due to the widespread implementation of DL methods in many fields. BNN and UQ predictions have gained more interest . BNN appVarious techniques have been proposed in medical image classification to detect tuberculosis (TB) in chest X-rays (CXRs).  presentsIn Ref. , an autoRef.  proposedIn Ref. , deep leRef.  utilizedRef.  suggesteThis section aims to provide a comprehensive overview of a lung cancer diagnosis method, its underlying techniques and procedures, as well as the recent advancements and challenges in this field. The primary objective is to evaluate the potential of using uncertainty quantification (UQ) in the context of medical image analysis, particularly for the purpose of enhancing the reliability of the diagnostic model.The study focuses on the use of Bayesian deep learning methods, specifically Baresnet, for the diagnosis of lung cancer. The dataset used in the study was obtained from LIDC-IDRI, a publicly available database that contains 244,527 images of 1010 cases. The images were obtained from clinical thoracic CT scans performed by four experienced thoracic radiologists.The images were annotated through a two-phase image annotation procedure and were available in various formats, including scalable vector graphics for screen-reading devices such as cell phones or tablets and XML for display on a computer or printer. The images showed extensive thickening of the lung nodules, most of which were concentrated at 1, 1.25, and 2.5 mm. After pre-processing, the sizes of the pulmonary nodules were expected to range from 3 mm to 30 mm, with a larger number of benign nodules having a small diameter and a smaller number of malignant nodules having a larger diameter.The XML commentary file for each patient made it possible to locate and assess the degree of malignancy in pulmonary nodules. Four radiologists reviewed the pulmonary nodules in the XML format and classified the degree of malignancy into five categories: highly unlikely for cancer, moderately unlikely for cancer, indeterminate likelihood, moderately suspicious for cancer, and highly suspicious of cancer. The first two categories were classified as non-malignant, while the last two categories were classified as malignant.In the field of medical image classification, convolutional neural networks (CNNs) have demonstrated remarkable success. However, a common challenge in training these models is the risk of overfitting, particularly with imbalanced datasets. To mitigate this issue, various techniques have been developed, including random sampling and L2 regularization . One sucIn conclusion, the paper describes different techniques for preventing overfitting in convolutional neural networks (CNNs) for medical image classification. It introduces DropOut, a regularization method that randomly drops out neurons during the forward pass of each training iteration, making the network more robust and less sensitive to individual neuron weights. DropConnect is another regularization technique that operates at the weight level by randomly zeroing out individual weights, reducing their contribution to the final prediction. The text then describes MC DropWeak, which combines DropOut and DropConnect, and has been shown to provide better results than either method alone by making the network more robust and reducing the risk of overfitting. The dropped weights and neurons can be reactivated during training if deemed essential to the accuracy of the predictions.p through the prior distribution, likelihood, and posterior steps, such as building an alpha-level Bayesian belief network (BBN) model. The posterior distribution provides information about the uncertain quantities in the Bayesian analysis as seen in Equation (1).The Bayesian classifier is a probabilistic method of classification that calculates the threshold parameters systematically through computation, as opposed to relying on a heuristically determined rule. It categorizes a pixel, x, as belonging to the sputum region if the probability of it being background (p(bg|x)) is lower than the probability of it being sputum (p(sp|x)). While traditional deep learning (DL) techniques have shown success in various real-world problems, they lack the ability to provide a measure of their predictions’ reliability. To address this issue, we utilized a Bayesian neural network (BNN) in our study. BNNs are models that incorporate probabilistic reasoning and represent random variables as independently and identically distributed inputs and one-hot encoded categorical outputs. BNNs can also identify uncertainties in classification problems and generate probabilistic predictions by computing complex mathematical computations. There are two types of uncertainty, aleatoric and epistemic, and the BNN model is formulated by considering the posterior distribution x^ “, “X”, and “Y^”. It represents the probability of observing these variables simultaneously, taking into account the relationship between them and a fourth variable “w”. The joint probability distribution is calculated as an integral over all the possible values of “w”. The integrand, PP, is the product of two probability distributions. The first, P, represents the joint probability of observing the variables “x^” and “w”, while the second, P, represents the joint probability of observing the variables “X” and “Y^”. The result of the integration is the joint probability distribution of all three variables “x^”, “X”, and “Y^”, considering the relationship between these variables and the variable “w”. This relationship between the variables can be interpreted as a form of uncertainty present in the system, which is represented by the variable “w”. The mutual information present in p is taken into account in the calculation of the joint probability distribution. It is important to note that averaging the predictions from an ensemble of neural networks based on the posterior distribution results in the same outcome as the distribution p. In other words, using an ensemble of neural networks allows us to incorporate the uncertainty present in the system and improve the accuracy of our predictions. This serves as a measure of bias-corrected epistemic uncertainty, reflecting the heterogeneity in the weight configurations predicted by the NNs, which depend on the estimated posteriors. This approach extracts an approximation of the finite bias from the population through entropy leave-one-out estimators, leading to a significant reduction in bias. The leave-one-out estimator is a resampling method used to evaluate the performance of a model by iteratively leaving out one sample and training the model on the remaining data. The prediction for the left-out sample is then compared with the actual value to compute the error. This process is repeated for each sample in the dataset and the errors are aggregated to obtain a measure of the model’s performance. In the context of Bayesian neural networks, the leave-one-out estimator can be used to estimate the finite bias present in the population by removing one sample at a time and computing the entropy of the predicted probabilities. This provides an approximation of the population’s bias, which can be used to reduce the overall bias in the predictions made by the NNs.The equation in question models the joint probability distribution of three variables: “This study aims to address the challenge of overfitting in medical image classification by utilizing transfer learning on a small dataset of CT scans. Specifically, the study fine-tunes a pre-trained ResNet-based Baresnet model, which includes a fully connected layer on top of the base ResNet layer and MC DropWeak for model uncertainty estimation. The study uses a combination of the Naïve Bayes classifier and ResNet to create Baresnet. The Naïve Bayes classifier is a straightforward probabilistic classifier that performs well with categorical variables, while ResNet is a deep learning neural network architecture for “Residual Networks.” The key innovation behind ResNet is the use of residual connections, which allow information to bypass multiple layers in the network and prevent vanishing gradients. The study also highlights the importance of the learning rate, a critical hyperparameter that determines the speed and convergence of the model. The environment for training these models typically involves a computing system with a GPU for acceleration and a large dataset of medical images, along with corresponding labels, for training and testing purposes.−5 and a factor of 0.2 and set the batch size to 16. The experiment was run for 750 epochs, and the validation accuracy was assessed after each epoch.The environment for training these models would typically involve a computing system with a GPU for acceleration and a large dataset of medical images, along with corresponding labels, for training and testing purposes. The learning rate is a crucial hyperparameter that determines the speed and convergence of the model. It is often set through trial and error and can significantly impact the model’s performance. To prevent overfitting, the study split the CT scan dataset into training (80%), testing (10%), and validation (10%) sets and performed real-time data augmentation. The images were rescaled to 256 × 256 pixels and standardized using the mean and standard deviation of the dataset. The study used the Adam optimizer with a learning rate of 1 × 10MC DropWeak was applied during training and Baresnet conducted Monte Carlo (MC) sampling by feeding the input image MC samples of 10, 25, and 50. MC DropWeak was added to the outputs of the FCL, allowing the model to dynamically change the drop probability per weight. The performance activation formula was expressed as follows in Equation (2).M” and “W” are used to generate multiple random realizations of some underlying process, and the function “f” is used to map these realizations to some output. The equation then approximates the output of “f” by taking the sum of the product of the matrices “M” and “W” for each realization and applying the function “f” to the result. The approximation in the equation is based on the law of large numbers, which states that the average of a large number of independent random variables converges to their expected value. The approximation assumes that the sum of the product of the matrices “M” and “W” for each realization represents a large number of independent random variables and that the result of the sum is close to their expected value.The equation is related to the Monte Carlo method. The Monte Carlo method is a statistical method that uses random sampling to estimate a function’s value or solve a problem. In the context of the equation provided, the matrices “M-bit binary string is mapped to the truth table representation of the function. The p-bit mask encodes the connection information drawn from a Bernoulli distribution with probability p. The weight between the jth neuron in layer l-1 and the ith neuron in layer l is represented by The p, which represents the probability of success. The probability of failure is simple (1 − p).The Bernoulli distribution is a fundamental concept in probability theory that has widespread applications in various fields, including statistics, machine learning, and data science. In its simplest form, the Bernoulli distribution models the probability of success and failure in a binary event, where success is represented by a value of 1 and failure is represented by a value of 0. The Bernoulli distribution is defined by a single parameter, The study demonstrates the effectiveness of transfer learning and MC DropWeak in addressing the challenge of overfitting in medical image classification. The study also highlights the importance of hyperparameters, such as the learning rate and the use of real-time data augmentation to prevent overfitting. The study provides insights into the use of ResNet and Baresnet architectures for medical image classification and their applications in the automated classification of lung cancer tumors using CT images. DropOut, DropConnect, and MC DropWeak are regularization techniques used to mitigate overfitting in CNNs. In medical image classification, MC DropWeak has been shown to provide better results than either DropOut or DropConnect alone. ResNet and Baresnet are deep learning architectures used in medical image classification, particularly for the automated classification of lung cancer tumors using CT images. The SoftMax layer generated the classmark probability distribution.Uncertainty quantification (UQ)  is an imIn ML, it is common to distinguish between two types of uncertainty: epistemic and aleatoric. Epistemic uncertainty refers to the uncertainty in the model parameters, which can be reduced with more training data. Aleatoric uncertainty, also known as data uncertainty, captures the observation noise and cannot be reduced with more data collection, but may be reduced with a more accurate sensor output. CT scans, commonly used in the diagnosis of lung cancer, have an epistemic degree of uncertainty that can be characterized using alternative probability distributions for discrete random variables and probability density functions for continuous variables.Data used in ML models are often small, incomplete, noisy, and multimodal, leading to a high degree of uncertainty in predictions made without proper UQ analysis. To achieve reliable results in DL, it is important to use the most robust and varied databases available, and to use UQ to understand the limitations of the model and the data used. The DL models used in lung cancer diagnosis and treatment, such as Baresnet, are structured to achieve specific performance targets, and the teaching process is replicated with new learning conditions to optimize the performance.In conclusion, UQ is essential in ML applications in lung cancer, providing valuable information about the degree of certainty in diagnosis and treatment decisions. By characterizing and quantifying uncertainty in the data and the models used, we can improve the reliability and accuracy of ML-based predictions in lung cancer.In the context of lung cancer, CT scans are commonly used for diagnosis and can have significant amounts of uncertainty associated with them. This uncertainty can stem from both the data itself and the models used to analyze the data. For instance, the CT scans may be noisy or of a low resolution, and the models used may not be well-calibrated or may not have seen similar data during training.By incorporating UQ techniques, we can account for both aleatoric and epistemic uncertainty in the CT scans and models. For example, probabilistic models can be used to represent aleatoric uncertainty by capturing the inherent noise in the observations. Meanwhile, Bayesian models can be used to represent epistemic uncertainty by characterizing our uncertainty about the model parameters.Additionally, UQ can also play a crucial role in model selection and validation. By quantifying uncertainty in the model predictions, we can better understand the reliability of different models and choose the one that is best suited for the task at hand. This can also help us identify cases where additional data or improved models are needed to achieve accurate predictions.Overall, the use of UQ in ML applications for lung cancer can help improve the accuracy and reliability of diagnosis and treatment decisions. By taking uncertainty into account, we can develop more robust and trustworthy ML-based tools for lung cancer diagnosis and treatment.In this study, we applied various methods to quantify the uncertainty in the predictive models used for lung cancer diagnosis and treatment decisions. These methods included the use of a predictive uncertainty estimator which measured the average standard deviation of the class probabilities for each class. However, this approach was not sufficient as it did not capture the full extent of uncertainty in the classification. To overcome this limitation, we introduced Bayesian methods for the estimation of uncertainty, using MC Dropweak during both the training and testing steps.Additionally, we studied two methods for measuring uncertainty in classification tasks: a tractable, dynamic model of mutual information (MI) and a bias-corrected model of MI. MI is a well-known measure of uncertainty that tests the difference between a prediction and the posterior distribution of a model’s parameters. We used the entropy of the predictive distribution as an uncertainty metric to compare the results of our approach with those of other competitors.Moreover, the optimization process not only helps to improve the accuracy of the predictions but also provides valuable information about the confidence in the predictions. This information is crucial in the context of medical applications as it can help to guide diagnosis and treatment decisions. In conclusion, incorporating UQ in the training process of the Baresnet model for lung cancer detection allows for a better representation of the inherent uncertainty in the data and the models, resulting in an improved reliability and accuracy of ML-based predictions.Overall, the uncertainty estimation of the Baresnet model’s predictions is the sum of two terms: the true mean of the system and the uncertainty caused by the uncertainty in the process and the error in the model itself. This highlights the importance of incorporating UQ in ML applications for lung cancer, as it provides valuable information about the degree of certainty in diagnosis and treatment decisions and helps to improve the reliability and accuracy of ML-based predictions, as seen in Equation (3).y) and its parameters (w) is calculated using the model’s epistemic uncertainty. The first term of the equation represents the entropy of the model’s predictions, which is critical when the predictions are inaccurate. The second term estimates the comparison between the entropy of the model’s predictions and the estimated posterior, taking into consideration the model’s parameters. This term, however, is unreliable in reflecting the model’s ability to account for the uncertainty associated with predictions made based on the estimated posteriors and weight configurations.Equation (3) seeks to optimize the mean reciprocal knowledge between the prediction made by the model and its posterior distribution. Essentially, it represents the amount of information gained about the model’s parameters by observing the model’s predictions for a given sample. The mutual information (MI) between the model’s output (As illustrated in To incorporate uncertainty quantification (UQ) in the Baresnet model, we employed MC Dropout and a Bayesian neural network (BNN). The results of the model’s loss and accuracy are visualized in In In the context of the study presented in The predictions were then evaluated for their uncertainty levels, and the accuracy threshold was calculated for values of 0.3 and 0.5.In Moreover, As displayed in Multimodality in the distribution of AUC is often the result of incorrect classifications. This can arise from the presence of irreducible homoscedastic and heteroscedastic noise in the data, which refers to random fluctuations in the measurement that cannot be reduced through repeated measurements. This type of noise can lead to inaccuracies in the model’s predictions, causing the distribution of the AUC to be multimodal. As a result, it is important to identify and address the sources of such noise to improve the performance and accuracy of the model.The results show that Baresnet with the MC Dropweak method achieved a sensitivity of 98.8 percent, surpassing other typical ML techniques, such as 2D CNN and RCNN, CNN, deep belief network, Boltzmann machine, extreme learning machine, and deep transfer, which demonstrated lower sensitivity results ranging from 82.2 to 97.9 percent. The results also indicate that Baresnet with the MC Dropweak method is more effective than other typical ML techniques and outperforms the other state-of-the-art methods, including those that use V-Net architecture, VGG16, ResNet50, Gaussian blur, and Otsu thresholding.In this study, a modified version of Baresnet was used for the detection of lung cancer in CT scan images. The model was designed to provide two forms of quantifiable uncertainties, which were aleatoric uncertainty and epistemic uncertainty. The results revealed a strong correlation between the model uncertainty and prediction accuracy, indicating the significance of incorporating uncertainty quantification techniques.Comparing Baresnet with other existing studies and popular deep learning methods, we found that Baresnet outperformed other techniques, especially when uncertainty quantification was incorporated. Our study highlighted the potential of the novel Baresnet architecture with uncertainty quantification techniques in improving the accuracy and diversity of the data samples for lung cancer detection.It is important to note that the use of traditional uncertainty estimation techniques is limited in accurately estimating uncertainty in lung segmentation, and our study demonstrates the advantages of using Baresnet with uncertainty quantification techniques in improving the reliability and trustworthiness of the predictions. As a limitation, it should be noted that in this study, we only tested our modified Baresnet model with one dataset for lung cancer classification. Although we have demonstrated promising results, the performance of the model on other datasets may vary. Future studies could investigate the generalizability of the model with different datasets and further validate the effectiveness of the uncertainty quantification techniques.In conclusion, this study demonstrates the potential of Baresnet with uncertainty quantification techniques in improving the accuracy of lung cancer detection. Future work will explore other model architectures to further improve the quality of epistemic uncertainty estimates. The findings of this study have significant implications for the clinical use of deep learning in lung cancer detection and can contribute to better patient outcomes.