Optimal filtering in the subband domain

An analytical framework for the implementation of optimal filters in the multiresolution (i.e., subband) domain is presented. In particular, we concentrate on filter bank based on the notions of wavelets and wave-packets. We show how the notion of sparse estimation can lead to significant reduction in computational cost, with only a minor degradation in performance. The combination of a wavelet-based filter bank with a sparse estimation scheme results in a configuration with five design parameters: (i) resolution level, (ii) degree of subband channel overlap, (iii) subband utilization ratio, (iv) estimation sparsity, and (v) filter order. We demonstrate the effect of each one of these design parameters on the over-all cost-performance trade-off