Optimum feedback quantizers for Laplacian pyramids

This paper addresses the problem of distortion allocation in a multi-layer image encoder based on an enhanced Laplacian pyramid with quantization noise feedback. An entropy-minimizing optimum quantization strategy is obtained by defining an equivalent memoryless pyramid entropy that, for the case of quantization feedback, is a function of rates and distortions at each pyramid level. By also modelling the propagation of quantization errors throughout the pyramid, a compact closed-form formulation is derived for the equivalent entropy. Such a model yields the optimum amounts of distortion at the various resolution layers, regardless of the first-order distributions of the data. Results are reported in terms of entropy for a Laplacian PDF varying with the quantization step sizes and the adjustable parameters of the pyramid-generating filters.