On optimality of JPEG2000 code stream

Arguably the most important and defining feature of JPEG 2000 image compression standard is its R-D optimized code stream of multiple progressive layers. This code stream is an interleaving of many scalable code streams of different sample blocks. In this paper we investigate the algorithms of optimizing the interleaving to minimize the expected distortion weighted by the probability distribution of operational rates in a given range, rather than for one or few fixed rates. We prove that the JPEG 2000 code stream constructed by EBCOT (embedded block coding of optimal truncation) is indeed optimal for uniform rate distribution function even if the individual scalable code streams have non-convex operational R-D curves. We also develop algorithms to optimize the JPEG 2000 code stream for exponential and Laplacian rate distribution functions.