Quantization noise feedback in Laplacian pyramid-based image coding: a rate-distortion approach

This paper addresses the problem of distortion allocation among layers in multi-resolution image encoders based on Laplacian pyramids with quantization noise feedback. An entropy-minimizing quantization strategy is obtained by defining an equivalent memoryless pyramid entropy that is a function of the rates and distortions at each pyramid level. By also modelling the propagation of quantization errors throughout the pyramid, a closed formulation is derived for entropy. Such a model yields the optimum amount of distortion to be allocated to a given pyramid layer, as a function of the variance of the coefficients on the overlying layer. Theoretical and experimental results in terms of pyramid entropy are compared varying with quantization step sizes and adjustable parameters of the pyramid-generating filters. Rate-distortion performance of a feedback-pyramid coder is compared with JPEG and shown to be fully superior.