Vector Set-Partitioning with Successive Refinement Voronoi Lattice VQ for Embedded Wavelet Image Coding

While lattice vector quantization (LVQ) can solve the complexity problem of LBG based vector quantizers, and also yield very general codebooks, a single stage lattice VQ, when applied to high variance vectors 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 paradigm is developed, where the codebooks in successive stages are all lattice codebooks, each in the shape of the Voronoi region of the lattice at the previous stage. The Voronoi shaped lattice codebook at each stage is called Voronoi lattice VQ (VLVQ). Measures of efficiency of successive refinement are developed. The developed methodology is applied to successively refine vectors of wavelet coefficients in the vector set-partitioning (VSPIHT) framework to obtain an embedded bitstream. The results are compared against the previous Successive Approximation Wavelet Vector Quantization (SA-W-VQ) results of Da Silva, Sampson and Ghanbari for image coding.