On $ell_1$ Data Fitting and Concave Regularization for Image Recovery.
Pré-print du CMLA 2012-04 - version du 15 mars 2012
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Auteurs : Mila Nikolova, Michael K. Ng and Chi-Pan Tam
Abstract :
We propose a new family of cost functions for signal and image recovery: they are composed of $ell_1$ data fitting term combined with concave regularization. We exhibit when and how to employ such cost functions.
Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems.
The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm.
All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions to solve specialized image recovery tasks.
We propose a new family of cost functions for signal and image recovery: they are composed of $ell_1$ data fitting term combined with concave regularization. We exhibit when and how to employ such cost functions.
Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems.
The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm.
All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions to solve specialized image recovery tasks.
- Type :
- Publication