Block based refitting in $\ell_{12}$ sparse regularisation
DELEDALLE, Charles-Alban
Institut de Mathématiques de Bordeaux [IMB]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
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Institut de Mathématiques de Bordeaux [IMB]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
DELEDALLE, Charles-Alban
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]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
VAITER, Samuel
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
< Reduce
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Language
en
Article de revue
This item was published in
Journal of Mathematical Imaging and Vision, 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019, 2019-06-30, Hofgeismar. 2021 n° 63, p. 216–236
Springer Verlag
English Abstract
In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to usel ...Read more >
In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to usel l(12) block-based regularization. While efficient at retrieving the inherent sparsity patterns of the data-the support-the estimated solutions are known to suffer from a systematical bias. We propose a general framework for removing this artifact by refitting the solution toward the data while preserving key features of its structure such as the support. This is done through the use of refitting block penalties that only act on the support of the estimated solution. Based on an analysis of related works in the literature, we introduce a new penalty that is well suited for refitting purposes. We also present a new algorithm 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 solutions of total variation and total generalized variation models.Read less <
English Keywords
Block sparsity
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