Image recovery via total variation minimization and related problems |
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Authors: | Antonin Chambolle Pierre-Louis Lions |
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Institution: | (1) Ceremade (CNRS, URA 749), Université de Paris-Dauphine, F-75775 Paris Cedex 16, France, FR |
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Abstract: | Summary. We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained
minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link
between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe
a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model
is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose
is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original
TV minimization problem that handles correctly some situations where TV fails.
Received December 21, 1995 / Revised version February 26, 1996 |
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Keywords: | Mathematics Subject Classification (1991):68U10 |
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