Rate-distortion-optimal subband coding without perfect-reconstruction constraints

We investigate the design of subband coders without the traditional perfect-reconstruction constraint on the filters. The coder uses scalar quantizers, and its filters and bit allocation are designed to optimize a rate-distortion criterion. Convexity properties play a central role in the analysis. Our results hold for a broad class of rate-distortion criteria. First, we show that optimality can be achieved using filter banks that are the cascade of a (paraunitary) principal component filter bank for the input spectral process and a set of pre- and post-filters surrounding each quantizer. Analytical expressions for the pre- and postfilters are derived. An algorithm for computing the globally optimal filters and bit allocation is given. We also develop closed-form solutions for the special case of two-channel coders under an exponential rate-distortion model. Finally, we investigate a constrained-length version of the filter design problem, which is applicable to practical coding scenarios. While the optimal filter banks are nearly perfect reconstruction at high rates, we demonstrate an apparently surprising advantage of optimal FIR filter banks: They significantly outperform optimal perfect-reconstruction FIR filter banks at all bit rates.