On optimal transforms for subband domain suppression of colored noise

Suppose we wish to analyze a noisy signal using a filter bank (FB) and apply noise suppression schemes such as Wiener filters in the subbands of the FB. This paper formalizes and studies the problem of finding the best FB for this purpose. The best FB depends on the class of allowed FB, the type of subband processing, and the statistics of the input signal and additive noise. Recently we have shown the optimality of the so-called principal component filter bank (PCFB) for several signal processing problems. In particular the PCFB is the optimum orthonormal FB for many schemes for suppression of white noise. With colored noise however the optimization is considerably more involved, and PCFB optimality is much more restricted. We present several results on the colored noise suppression problem. We develop an algorithm to find the exact globally optimum unconstrained orthonormal FB for piecewise constant input signal and noise spectra. This thus allows approximation of the optimum FB for any spectra to any desired accuracy. We examine the role of PCFB in the optimization.