Optimal transform for colored noise suppression

There has been interest in the application of filter banks and transforms to noise suppression. Recently, Akkarakaran and Vaidyanathan (2001) showed that when the noise is white, the optimal transform (not necessary unitary) for noise suppression is the Karhunen-Loeve transform (KLT). Moreover they showed that for the case of colored noise, if both the noise and signal have a common KLT, then the KLT is optimal for subband noise suppression. In this paper, we derive the optimal transform (not restricting to the class of unitary transforms) for the noise suppression problem when the signal and noise have arbitrary spectrum.