Successive refinement lattice vector quantization

Lattice vector quantization (LVQ) solves the complexity problem of LBG based vector quantizers, yielding very general codebooks. However, a single stage LVQ, when applied to high resolution quantization of a vector, may result in very large and unwieldy indices, making it unsuitable for applications requiring successive refinement. The goal of this work is to develop a unified framework for progressive uniform quantization of vectors without having to sacrifice the mean- squared-error advantage of lattice quantization. A successive refinement uniform vector quantization methodology is developed, where the codebooks in successive stages are all lattice codebooks, each in the shape of the Voronoi regions of the lattice at the previous stage. Such Voronoi shaped geometric lattice codebooks are named Voronoi lattice VQs (VLVQ). Measures of efficiency of successive refinement are developed based on the entropy of the indices transmitted by the VLVQs. Additionally, a constructive method for asymptotically optimal uniform quantization is developed using tree-structured subset VLVQs in conjunction with entropy coding. The methodology developed here essentially yields the optimal vector counterpart of scalar "bitplane-wise" refinement. Unfortunately it is not as trivial to implement as in the scalar case. Furthermore, the benefits of asymptotic optimality in tree-structured subset VLVQs remain elusive in practical nonasymptotic situations. Nevertheless, because scalar bitplane- wise refinement is extensively used in modern wavelet image coders, we have applied the VLVQ techniques to successively refine vectors of wavelet coefficients in the vector set-partitioning (VSPIHT) framework. The results are compared against SPIHT and the previous successive approximation wavelet vector quantization (SA-W-VQ) results of Sampson, da Silva and Ghanbari (1996).