Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Study in the BV Space of a Denoising—Deblurring Variational Problem

A Study in the BV Space of a Denoising—Deblurring Variational Problem . In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using lower semicontinuity results for convex functionals of measures. We also give a new and fine characterization of the subdifferential of the functional, together with optimality conditions on the solution, using duality techniques of Temam for the theory of time-dependent minimal surfaces. We study the associated evolution equation in the context of nonlinear semigroup theory and we give an approximation result in continuous variables, using Γ -convergence. Finally, we discretize the problems by finite differences schemes and we present several numerical results for signal and image reconstruction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics & Optimization Springer Journals

A Study in the BV Space of a Denoising—Deblurring Variational Problem

Vese, L.
Applied Mathematics & Optimization , Volume 44 (2) – Jan 1, 2001
Download PDF
31 pages

Loading next page...
 
/lp/springer_journal/a-study-in-the-bv-space-of-a-denoising-deblurring-variational-problem-P1gnI96Dq8

References (32)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag New York Inc. 2001
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-001-0017-7
Publisher site
See Article on Publisher Site

Abstract

. In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using lower semicontinuity results for convex functionals of measures. We also give a new and fine characterization of the subdifferential of the functional, together with optimality conditions on the solution, using duality techniques of Temam for the theory of time-dependent minimal surfaces. We study the associated evolution equation in the context of nonlinear semigroup theory and we give an approximation result in continuous variables, using Γ -convergence. Finally, we discretize the problems by finite differences schemes and we present several numerical results for signal and image reconstruction.

Journal

Applied Mathematics & Optimization – Springer Journals

Published: Jan 1, 2001

Keywords: Variational methods; Elliptic/parabolic PDEs; Functions of bounded variation; Convex functions of measures; Duality; Relaxation; Maximal monotone operators; Γ -Convergence; Finite differences scheme; Signal and image processing; AMS Classification. 35, 49, 65.

There are no references for this article.