Maximum Likelihood Identification of Multiscale Stochastic Models Using the Wavelet Transform and the Em Algorithm

Spurred by the emerging theory of multiscale representations of signals and wavelet transforms, researchers in the signal and image processing community have developed multiresolution processing algorithms. These algorithms have promise because they are computa-tionally eecient, especially in 2D, and because they are applicable to a wide variety of processes, including 1=f processes. In this paper we address the problem of estimating the parameters of a class of multi-scale stochastic processes that can be modeled by state-space dynamic systems driven by white noise in scale rather than in time. We present a MaximumLikelihood identiication method for estimating the parameters of our multiscale stochastic models given data which is based on the wavelet transform and the Expectation-Maximization algorithm.