Design and performance of tree-structured vector quantizers

Abstract

The design of vector quantizers (VQ) involves the partitioning of a multidimensional space into a finite number of regions. It is desired but generally difficult to find the partition that minimizes the expected distortion subject to a cost constraint. Tree-structured vector quantization (TSVQ) reduces the complexity by imposing a hierarchical structure on the partitioning. We study the design of optimal tree-structured vector quantizers that minimize the expected distortion subject to cost functions related to storage cost, encoding rate, or quantization time. The optimal design problem is shown to be intractable in most cases, and heuristic techniques have to be used. We analyze the performance of a general design heuristic based on successive partitioning, and propose a recursively descend optimization criterion for the algorithm. Experimental results in image compression show the new criterion performs favorably compared with existing ones.