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Approximating the total variation with finite differences or finite elements

Chambolle, Antonin; Pock, Thomas (2021), Approximating the total variation with finite differences or finite elements, in Andrea Bonito, Ricardo H. Nochetto, Handbook of Numerical Analysis: Geometric Partial Differential Equations II, volume 22, Elsevier : Amsterdam, p. 383-417. 10.1016/bs.hna.2020.10.005

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Type
Chapitre d'ouvrage
Date
2021
Book title
Handbook of Numerical Analysis: Geometric Partial Differential Equations II, volume 22
Book author
Andrea Bonito, Ricardo H. Nochetto
Publisher
Elsevier
Published in
Amsterdam
ISBN
9780444643056
Number of pages
544
Pages
383-417
Publication identifier
Metadata
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Author(s)
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Pock, Thomas
Institute for Computer Graphics and Vision [Graz] [ICG]
Abstract (EN)
We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, of a gray-level image in two dimensions). We discuss the properties of finite differences and finite elements based approach and compare their merits, in particular in terms of error estimates and quality of the reconstruction.
Subjects / Keywords
Image processing; numerical analysis; total variation; finite differences; finite elements; error bounds