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.
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Accepted 5 March 2001. Online publication 20 June 2001.
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Vese, L. A Study in the BV Space of a Denoising—Deblurring Variational Problem. Appl Math Optim 44, 131–161 (2001). https://doi.org/10.1007/s00245-001-0017-7
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DOI: https://doi.org/10.1007/s00245-001-0017-7