Generalized Wiener estimation algorithms based on a family of heavy-tail distributions

A fundamental problem in signal processing is to estimate signal from noisy observations. When some prior information about the statistical models of the signal and noise is available, the estimation problem can be solved by using the maximum a posteriori (MAP) principle. In this paper, we develop an EM algorithm for the MAP estimate of signals modeled by a family of heavy-tail prior distributions: Laplacian, student-t and slash. We establish links between the EM algorithm and the Wiener estimation. We then modify the EM algorithm and propose two generalized Wiener estimation algorithms for image denoising. Experimental results show that the performance of the proposed algorithms is better than that of the bi-shrinkage algorithm which is arguably one of the best in recent publications.