Image Denoising using Dual Formulations

Arnaud Le Carvennec

Semester Master Project

ENS Cachan, France, EPFL

January 2010

Abstract

In this project we want to investigate denoising and deconvolution methods that use a well-known variational approach (i.e., l1 regularization), but that involves a specific regularization operator (i.e., the Laplacian). In a first part, we present the dual-TV method that is often used in denoising and deconvolution, and on which we base our (slightly different) algorithmic approach for dual-Laplacian denoising. In a second step we expose the theorical foundations of our method, and show the implementation that can be deduced from that approach. In the last part of this report, we compare the performance of our deconvolution method (in terms of SNR and visual quality) with respect to TV and to L2-deconvolution. We show several results in 1D, 2D and 3D.