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. Using convexity analysis, we show that optimality can be achieved using filterbanks that are the cascade of a (paraunitary) principal component filterbank for the input spectral process and a set of pre and postfilters surrounding each quantizer. Analytical expressions for the pre and postfilters are then 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 filterbanks are nearly perfect-reconstruction at high rates, we demonstrate an apparently surprising advantage of optimal FIR filterbanks; they significantly outperform optimal perfect-reconstruction FIR filterbanks at all bit rates.