An investigation of wavelet-based image coding using an entropy-constrained quantization framework

Wavelet image decompositions generate a tree-structured set of coefficients, providing an hierarchical data-structure for representing images. Several recently proposed image compression algorithms have focused on new ways for exploiting dependencies between this hierarchy of wavelet coefficients. This paper presents a new framework for understanding the efficiency of one such algorithm as a simplified attempt to a global entropy-constrained image quantizer. The principle insight offered by the new framework is that improved performance is achieved by more accurately characterizing the joint probabilities of arbitrary sets of wavelet coefficients. The specific algorithm described is designed around one conveniently structured collection of such sets. The efficiency of hierarchical wavelet coding algorithms derives from their success at identifying and exploiting dependencies between coefficients in the hierarchical structure. The second part of the paper presents an empirical study of the distribution of high-band wavelet coefficients, the band responsible for most of the performance improvements of the new algorithms