Why does histogram packing improve lossless compression rates?

The performance of state-of-the-art lossless image coding methods [such as JPEG-LS, lossless JPEG-2600, and context-based adaptive lossless image coding (CALIC)] can be considerably improved by a recently introduced preprocessing technique that can be applied whenever the images have sparse histograms. Bitrate savings of up to 50% have been reported, but so far no theoretical explanation of the fact has been advanced. This letter addresses this issue and analyzes the effect of the technique in terms of the interplay between histogram packing and the image total variation, emphasizing the lossless JPEG-2000 case.