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 and Optimization Springer Journals

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

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 2001 Springer-Verlag New York
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
D.O.I.
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 and OptimizationSpringer Journals

Published: Jan 1, 2001

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