An introduction to continuous optimization for imaging

作者：Chambolle, Antonin^*; Pock, Thomas

来源：Acta Numerica, 2016, 25: 161-319.

DOI：10.1017/S096249291600009X

• TOTAL VARIATION MINIMIZATION
• PROXIMAL POINT ALGORITHM
• CONSTRAINED TOTAL VARIATION
• ALTERNATING DIRECTION METHOD
• VECTORIAL TOTAL VARIATION
• PRIMAL-DUAL ALGORITHMS
• MONOTONE-OPERATORS
• THRESHOLDING ALGORITHM
• CONVERGENCE ANALYSIS
• DESCENT METHODS

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.

• 出版日期2016