The Rayleigh-Ritz Method for Total Variation Denoising

Leopold Matamba Messi
Mathematical Biosciences Institute, The Ohio State University

(November 1, 2012 10:20 AM - 11:15 AM)

The Rayleigh-Ritz Method for Total Variation Denoising

Abstract

In total variation denoising, one attempts to enhance an image by solving a constrained minimization problem with a total variation objective. The method has proven very effective at smoothing functions with discontinuities. More recently, it was also shown that such a model is capable of preserving regularity of the data. In this talk, I will present a convergent Rayleigh-Ritz method for approximating the smooth solutions of the L^2 total variation denoising model. The proof exploits the properties of functions of bounded variation, the approximation power of spline functions, and the non-expansiveness of the TV-denoising operator.