Histogram packing, total variation, and lossless image compression

State-of-the-art lossless image compression methods, such as JPEG-LS, lossless JPEG-2000, and CALIC, perform considerably better on images with sparse histograms when a recently introduced preprocessing technique is used. Bitrate savings of up to 50% have been reported, but so far there is no firm theoretical foundation for this surprising performance. In this paper we address this issue, and attempt to explain how the preprocessing stage, which basically packs the histogram of the images, affects the image total variation, and as a result the ability of the compression algorithms to work more effectively.