Abstract
A large number of imaging problems reduce to the optimization of a cost function, with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification.
Originalsprache | englisch |
---|---|
Seiten (von - bis) | 161-319 |
Seitenumfang | 159 |
Fachzeitschrift | Acta Numerica |
Jahrgang | 25 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Mai 2016 |
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ASJC Scopus subject areas
- Numerische Mathematik
- !!Mathematics(all)
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An introduction to continuous optimization for imaging. / Chambolle, Antonin; Pock, Thomas.
in: Acta Numerica, Jahrgang 25, 01.05.2016, S. 161-319.Publikation: Beitrag in einer Fachzeitschrift › Review eines Fachbereichs (Review article) › Forschung › Begutachtung
}
TY - JOUR
T1 - An introduction to continuous optimization for imaging
AU - Chambolle, Antonin
AU - Pock, Thomas
PY - 2016/5/1
Y1 - 2016/5/1
N2 - A large number of imaging problems reduce to the optimization of a cost function, with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification.
AB - A large number of imaging problems reduce to the optimization of a cost function, with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification.
UR - http://www.scopus.com/inward/record.url?scp=84983656005&partnerID=8YFLogxK
U2 - 10.1017/S096249291600009X
DO - 10.1017/S096249291600009X
M3 - Review article
VL - 25
SP - 161
EP - 319
JO - Acta Numerica
JF - Acta Numerica
SN - 0962-4929
ER -