Statistical signal restoration with 1/ f wavelet domain prior models

Abstract

In this paper we examine the problem of estimating a stochastic signal from noise corrupted linearly distorted samples of the original. Due to the ill-posedness caused by the blurring function, we are motivated to examine an inversion method in which the statistics of the underlying process are modeled as a 1/ f type fractal process. In particular, we explore two issues with the use of such a model: the effects of model mismatch and parameter estimation. Our analysis demonstrates that the mean-square-error performance of the estimator is quite insensitive to the choice of prior model parameters used in the recovery of the signal. Such robustness is shown to hold even when the underlying process is not of the 1/ f variety. We then introduce an expectation–maximization technique for jointly extracting the best parameters for use in an inversion along with the reconstructed signal. Here, Monte Carlo and Cramer–Rao bound results demonstrate that we are able to determine accurate model parameters exactly in those situations where the model mismatch analysis shows that such fidelity is required to ensure low mean square error in the recovery of the underlying signal.