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. A new class of previously proposed image compression algorithms has focused on new ways for exploiting dependencies between this hierarchy of wavelet coefficients using "zero-tree" data structures. This paper presents a new framework for understanding the efficiency of one specific algorithm in this class we introduced previously and dubbed the space-frequency quantization (SFQ)-based coder. It describes, at a higher level, how the SFQ-based image coder of our earlier work can be construed as a simplified attempt to design a global entropy-constrained vector quantizer (ECVQ) with two noteworthy features: (i) it uses an image-sized codebook dimension (departing from conventional small-dimensional codebooks that are applied to small image blocks); and (ii) it uses an on-line image-adaptive application of constrained ECVQ (which typically uses off-line training data in its codebook design phase). The principal 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. We also present an empirical statistical study of the distribution of the wavelet coefficients of high-frequency bands, which are responsible for most of the performance gain of the new class of algorithms. This study verifies that the improved performance achieved by the new class of algorithms like the SFQ-based coder can be attributed to its being designed around one conveniently structured and efficient collection of such sets, namely, the zero-tree data structure. The results of this study further inspire the design of alternative, novel data structures based on nonlinear morphological operators.