<sod>Image reconstruction and image scaling/interpolation can be also interpreted as [[resampling]] under consideration of the [[Nyquist theorem]] sampling theorem. According to the theorem the downsampling to the 40x40 thumbnail image from the 160x160 original image should be only carried out only after applying a suitable 2D [[lowpass filter]] to prevent aliasing artifacts. If this is done, the downsampling step by factor four is lossless (the information loss happened with filtering) and can be reconstructed (beside rounding errors) lossless again back to the 160x160 image ("reconstruction/ image scaling"). The last image shows the aliasing artifacts happening if a lowpass filter is not applied in this process.<eod>
<sod>Image reconstruction and image scaling/interpolation can be also interpreted as [[resampling]] under consideration of the [[Nyquist theorem]] sampling theorem. According to the theorem the downsampling to the 40x40 thumbnail image from the 160x160 original image should be only carried out only after applying a suitable 2D [[lowpass filter]] to prevent aliasing artifacts. The image is reduced to the informations which can be carried by the smaller image, 1/16 in this case. As natural images have their information clustered on the lower spatial frequencies the effective information loss is significant smaller (a property also [[JPEG]] compression relies on). If this is done, the downsampling step by factor four is lossless (the information loss happened with filtering) and can be reconstructed ("interpolation / image scaling") lossless (beside rounding errors) again back to the 160x160 filtered image or any other resolution. The last image shows the aliasing artifacts happening if a lowpass filter is not applied in this process.<eod>