Entropy coded successively refinable uniform threshold quantizers

We examine the performance of entropy coded successively refinable uniform threshold quantizers, which have been utilized in numerous proposed progressive image coders. We view a successively refinable quantizer with N stages of refinement as consisting of a sequence of partitions {Pⁿ}, and a sequence of codebooks {Cⁿ}, 1⩽n⩽N. We denote the n^th reconstruction of an input sample x as xⁿ; it can be obtained using the n^th partition and n^th codebook and a simple quantization rule. We consider the design of entropy-coded successively refinable scalar quantizers in which the finest (highest rate) partition and corresponding codebook comprise a uniform threshold quantizer (UTQ). All codebooks are designed optimally for the corresponding partitions and it is well known that entropy coded UTQs perform within 0.255 bits/sample of the rate distortion bound for a variety of source distributions