Communications in Mathematical Sciences

Volume 12 (2014)

Number 5

A few remarks on variational models for denoising

Pages: 843 – 857

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n5.a3

Authors

Rustum Choksi (Department of Mathematics and Statistics, McGill University, Montreal, Canada)

Irene Fonseca (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Barbara Zwicknagl (Institut für Angewandte Mathematik, Universität Bonn, Germany)

Abstract

Variational models for image and signal denoising are based on the minimization of energy functionals consisting of a fidelity term together with higher-order regularization. In addition to the choices of function spaces to measure fidelity and impose regularization, different scaling exponents appear. In this note we present a few simple remarks on (i) the stability with respect to deterministic noise perturbations, captured via oscillatory sequences converging weakly to zero, and (ii) exact reconstruction.

Keywords

denoising, higher-order regularization, stability, weak convergence, Brezis-Lieb condition

2010 Mathematics Subject Classification

49N25, 94A08

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