Robust multiscale representation of processes and optimal signal reconstruction

We propose a statistical approach to obtain a “best basis” representation of an observed random process. We derive statistical properties of a criterion first proposed to determine the best wavelet packet basis, and, proceed to use it in constructing a statistically sound algorithm. For signal enhancement, this best basis algorithm is followed by a nonlinear filter based on the minimum description length (MDL) criterion. We show that it is equivalent to a min-max based algorithm proposed by Donoho and Johnstone (1992)