EM algorithms for robust signal filtering and prediction

Transform domain denoising, noise filtering based on data from a local neighborhood and linear prediction are three important signal processing tasks. In this paper we treat these tasks from a maximum a posteriori estimation (MAP) perspective and address the problem of robust estimation. The Student-t and Laplacian distributions are used to model the noise to permit robustness to outliers. Independent Gaussian distributions with different variances are used as the prior distributions for the parameters to be estimated. This provides a mechanism to incorporate into the solution certain desirable properties such as the sparseness constrain in transform domain denoising and regularization in linear prediction. EM algorithms are developed for the three signal processing tasks. Applications are demonstrated.