On optimization of filter banks with denoising applications

The problem of optimization of subband coders for given input statistics has received considerable attention in recent literature. The goal in these works has been to maximize the coding gain, which is a compression performance measure under the standard quantizer noise models for high bit-rates. The optimal filter bank (FB) for this problem has been observed to be a principal component filter bank (PCFB) for the class of FBs over which the optimization is performed. The purpose of this paper is to point out a stronger connection between optimality of the FB and the principal component property, which appears to have been overlooked in the literature. We show that PCFBs are also optimal for a variety of other signal processing schemes such as noise suppression by using hard-thresholding or zeroth order Wiener filtering in the subbands.