Optimal subband decoding

This paper addresses the question of optimal subband decoding, given a system of subband analysis filters and a predetermined quantization strategy. Optimal analysis-synthesis pairs are of great interest, but have been characterized only under very strong (and impractical) conditions. Limiting our attention to the decoder, we find optimal synthesis filters by solving a system of regression equations. Neither high-rate quantization, whiteness of the quantization noise, nor optimality of the quantizer is assumed. Optimal coefficients are independent of the internal machinery of the quantizers, and can therefore be used with "canned" software packages. Only knowledge of the analysis filter bank is assumed. Preliminary experiments show modest gains, on the order of 0.1-0.3 dB, by applying this method to one-stage reproduction of natural images from zerotree quantizers.