Time Frequency Brown Bag Seminar

Wednesday, February 24, 1999

12:30pm

EQuad E415

Speaker: Hamid Krim, ECE Department, North Carolina State University

Title: Multiscale Denoising: Beyond the Normal Noise Assumption

Abstract: Approaches to wavelet-based denoising (or signal enhancement) have generally relied on the assumption of normally distributed perturbations. We give a very brief overview of the existing results and proceed to relax the noise normality assumption, which is often violated in practice. We derive a robust wavelet thresholding technique based on the Minimax Description Length (MMDL) principle. We first determine the least favorable distribution in the ε-contaminated normal family as the member that maximizes the entropy. We show that this distribution and the associated maximum likelihood estimator, together meet the Minimax condition. The MMDL approach results in a thresholding scheme that is resistant to heavy-tailed noise. We further extend this framework and propose a novel approach to selecting an adapted or Best Basis (BB) that results in optimal signal reconstruction. Finally, we address the practical case where the underlying signal is known to be bounded, and derive a two-sided thresholding technique that is resistant to outliers and has bounded error. We briefly contrast these techniques to other variational techniques which we argue may provide a better alternative for excessively noisy environments, based on some of our recent results on probabilistic variational approaches.