An introduction to continuous optimization for imaging. (23rd May 2016)

• Record Type: Journal Article
• Authors: Chambolle, Antonin; Pock, Thomas
• Is Part Of: Acta numerica. Volume 25(2016)
• Page Start: 161
• Page End: 319
• Publication Date: 2016-05-23
• Subjects: Numerical analysis -- Periodicals; 518
• DOI: 10.1017/S096249291600009X
• Languages: English
• ISSNs: 0962-4929

Abstract

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.