The Role of Principal Component Filter Banks in Noise Reduction

The purpose of this paper is to demonstrate the optimality properties of principal component filter-banks for various noise reduction schemes. Optimization of filter-banks (FB’s) for coding gain maximization has been carried out in the literature, and the optimized solutions have been observed to satisfy the principal component property, which has independently been studied. Here we show a strong connection between the optimality and the principal component property; which allows us to optimize FB’s for many other objectives. Thus, we consider the noise-reduction scheme where a noisy signal is analyzed using a FB and the subband signals are processed either using a hard-threshold operation or a zeroth order Wiener filter. For these situations, we show that a principal component FB is again optimal in the sense of minimizing the expected mean-square error.