Wavelets and random processes: optimal matching in the Bhattacharyya sense

The use of wavelet packet bases to represent deterministic signals has led to optimal representations that minimize a desired cost function. In this paper we present an algorithm that uses wavelet packet bases to construct a random process that is matched to an arbitrary correlation matrix. An analytical expression for the Bhattacharyya coefficient gauges the similarity between the two processes and leads to two iterative algorithms that are used jointly to find the desired quantities. Eigen-decompositions for the two processes reduce the problem to finding the best wavelet-based unitary matrix and a set of eigenvalues. Examples illustrates the technique.