A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

• Published in: Journal of mathematical imaging and vision Vol. 40; no. 1; pp. 120 - 145
• Main Authors: Chambolle, Antonin, Pock, Thomas
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.05.2011
• Subjects: Applications of Mathematics; Computer Science; Image Processing and Computer Vision; Mathematical Methods in Physics; Signal,Image and Speech Processing; Reconstruction; Total variation; Dual approaches; Inverse problems; Image; Convex optimization

In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O (1/ N ) in finite dimensions for the complete class of problems. We further show accelerations of the proposed...