Optimal Coding of Quantized Laplacian Sources for Predictive Image Compression

This paper discusses the optimal coding of uniformly quantized Laplacian sources. The techniques known for designing optimal codes for sources with infinite alphabets are used for the quantized Laplacian sources which have probability mass functions with two geometrically decaying tails. Due to the simple parametric model of the source distribution the Huffman iterations are possible to be carried on analytically, using the concept of reduced source, and the final codes are obtained as a sequence of very simple arithmetic operations, avoiding the need to store coding tables. Comparing three uniform quantizers, we find one which consistently outperforms the others in the rate-distortion sense. We foresee for the newly introduced codes an important area of applications in low complexity lossy image coding, since similar codes, designed for two-sided geometrical sources, became the basic tools used in JPEG-LS lossless image compression.