Result: Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems

Title:
Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems
Authors:
de Castro, Yohann, Duval, Vincent, Petit, Romain
Contributors:
Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Probabilités, statistique, physique mathématique (PSPM), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work was supported by a grant from Région Ile-De-France and by the ANR CIPRESSI project, grant ANR-19-CE48-0017-01 of the French Agence Nationale de la Recherche., Elmoataz, Abderrahim, Fadili, Jalal, Quéau, Yvain, Rabin, Julien, Simon, Loïc, ANR-19-CE48-0017,CIPRESSI,Traitement d'images continues: modèles et algorithmes(2019)
Source:
Scale Space and Variational Methods in Computer Vision ; https://inria.hal.science/hal-03196916 ; Elmoataz, Abderrahim; Fadili, Jalal; Quéau, Yvain; Rabin, Julien; Simon, Loïc. Scale Space and Variational Methods in Computer Vision, 12679, Springer, Cham, pp.553-564, 2021, Lecture Notes in Computer Sciences, ⟨10.1007/978-3-030-75549-2_44⟩
Publisher Information:
CCSD
Springer, Cham
Publication Year:
2021
Subject Terms:
Total variation, Inverse problems, Off-the-grid imaging, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing
Document Type:
Book book part
Language:
English
Relation:
https://inria.hal.science/hal-03406710v3; info:eu-repo/semantics/altIdentifier/arxiv/2104.06706; ARXIV: 2104.06706
DOI:
10.1007/978-3-030-75549-2_44
Availability:
https://inria.hal.science/hal-03196916
https://inria.hal.science/hal-03196916v2/document
https://inria.hal.science/hal-03196916v2/file/main.pdf
https://doi.org/10.1007/978-3-030-75549-2_44
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edsbas.A714C36B
Database:
BASE

Further Information

International audience ; We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed mesh, our approach exploits the structure of the solutions and consists in iteratively constructing a linear combination of indicator functions of simple polygons.