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Image recovery via total variation minimization and related problems

Chambolle, Antonin; Lions, Pierre-Louis (1997), Image recovery via total variation minimization and related problems, Numerische Mathematik, 76, 2, p. 167-188. http://dx.doi.org/10.1007/s002110050258

Type
Article accepté pour publication ou publié
Date
1997
Journal name
Numerische Mathematik
Volume
76
Number
2
Publisher
Springer
Pages
167-188
Publication identifier
http://dx.doi.org/10.1007/s002110050258
Metadata
Show full item record
Author(s)
Chambolle, Antonin cc
Lions, Pierre-Louis
Abstract (EN)
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.
Subjects / Keywords
TV minimization problem; image denoising technique

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