Optimal hierarchical decompositions for signals coded using Lloyd-Max quantizers

Optimal hierarchical coding is sought, for progressive or scalable image transmission, by minimizing the variance of the error difference between the original image and its lower resolution renditions. The optimal, according to the above criterion, pyramidal and subband image coders are determined for images quantized using the optimal vector Lloyd-Max quantizers. A rigorous statistical model of a vector Lloyd-Max quantizer is established first, consisting of a linear time-invariant filter followed by additive noise uncorrelated with the input. Experimental results illustrate the implementation and performance of the optimal coders.