ICASSP 2016
Pedram Pad, EPFL STI LIB

Test Run • 15 March 2016 • BM 4 233

Abstract
Title 1: Optimal Isotropic Wavelets for Localized Tight Frame Representations Abstract 1: In this paper, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known. Title 2: MMSE Denoising of Sparse and Non-Gaussian AR(1) Processes Abstract 2: We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is an iterative algorithm that combines standard wavelet-based thresholding with an optimized non-linearity and cycle-spinning. This method is more computationally efficient than the former and appears to provide the same optimal denoising results in practice. We illustrate the superior performance of both methods through numerical simulations by comparing them with other wellknown denoising schemes.