Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties
DELEDALLE, Charles-Alban
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
Institut de Mathématiques de Bordeaux [IMB]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
Institut de Mathématiques de Bordeaux [IMB]
PAPADAKIS, Nicolas
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
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Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
DELEDALLE, Charles-Alban
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
Institut de Mathématiques de Bordeaux [IMB]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
Institut de Mathématiques de Bordeaux [IMB]
PAPADAKIS, Nicolas
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
VAITER, Samuel
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Centre National de la Recherche Scientifique [CNRS]
< Reduce
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Centre National de la Recherche Scientifique [CNRS]
Language
en
Chapitre d'ouvrage
This item was published in
Scale Space and Variational Methods in Computer Vision, Scale Space and Variational Methods in Computer Vision. 2019-06-05, vol. 11603, p. 131-143
English Abstract
In inverse problems, the use of an l(12) analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained ...Read more >
In inverse problems, the use of an l(12) analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good behavior of the proposed block penalty for refitting.Read less <
English Keywords
Total variation
Bias correction
Refitting
European Project
Nonlocal Methods for Arbitrary Data Sources
ANR Project
Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010
Origin
Hal imported