An introduction to continuous optimization for imaging

Antonin Chambolle, Thomas Pock

Research output: Contribution to journalReview articleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)161-319
Number of pages159
JournalActa Numerica
Volume25
DOIs
Publication statusPublished - 1 May 2016

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Continuous Optimization
Imaging
Imaging techniques
Optical flows
Scale Function
Magnetic resonance
Deblurring
Stereo Matching
Image segmentation
Cost functions
Optical Flow
Magnetic Resonance Imaging
Structural properties
Denoising
Interconnection
Image Segmentation
Structural Properties
Cost Function
Optimization Methods
Objective function

ASJC Scopus subject areas

  • Numerical Analysis
  • Mathematics(all)

Cite this

An introduction to continuous optimization for imaging. / Chambolle, Antonin; Pock, Thomas.

In: Acta Numerica, Vol. 25, 01.05.2016, p. 161-319.

Research output: Contribution to journalReview articleResearchpeer-review

Chambolle, Antonin ; Pock, Thomas. / An introduction to continuous optimization for imaging. In: Acta Numerica. 2016 ; Vol. 25. pp. 161-319.
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