Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties
| Autor: | Charles-Alban Deledalle, Samuel Vaiter, Nicolas Papadakis, Joseph Salmon |
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| Přispěvatelé: | Department of Electrical and Computer Engineering [Univ California San Diego] (ECE - UC San Diego), University of California [San Diego] (UC San Diego), University of California (UC)-University of California (UC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE33-0010,GOTMI,Generalized Optimal Transport Models for Image processing(2016), European Project: 777826,NoMADS(2018), Department of Electrical and Computer Engineering - University of California San Diego, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB) |
| Rok vydání: | 2019 |
| Předmět: |
Artifact (error)
Total variation Computer science Regular polygon 02 engineering and technology Inverse problem 01 natural sciences [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] 010104 statistics & probability Refitting 0202 electrical engineering electronic engineering information engineering Bias correction 020201 artificial intelligence & image processing 0101 mathematics [MATH]Mathematics [math] Algorithm Block (data storage) |
| Zdroj: | Scale Space and Variational Methods in Computer Vision-7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 – July 4, 2019, Proceedings Lecture Notes in Computer Science Lecture Notes in Computer Science-Scale Space and Variational Methods in Computer Vision Scale Space and Variational Methods in Computer Vision Scale Space and Variational Methods in Computer Vision, 11603, pp.131-143, 2019, 978-3-030-22367-0. ⟨10.1007/978-3-030-22368-7_11⟩ Lecture Notes in Computer Science ISBN: 9783030223670 SSVM |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-030-22368-7_11 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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