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A first-order primal-dual algorithm for convex problems with applications to imaging (2010)
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BibTeX
@MISC{Chambolle10afirst-order,
author = {Antonin Chambolle and Thomas Pock},
title = {A first-order primal-dual algorithm for convex problems with applications to imaging},
year = {2010}
}
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Abstract
In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering in this paper. We further show accelerations of the proposed algorithm to yield optimal rates on easier problems. In particular we show that we can achieve O(1/N 2) convergence on problems, where the primal or the dual objective is uniformly convex, and we can show linear convergence, i.e. O(1/e N) on problems where both are uniformly convex. The wide applicability of the proposed algorithm is demonstrated on several imaging problems such as image denoising, image deconvolution, image inpainting, motion estimation and image segmentation. 1
Keyphrases
first-order primal-dual algorithm convex problem uniformly convex wide applicability finite dimension image segmentation optimal rate dual objective complete class linear convergence image denoising saddle-point structure motion estimation image deconvolution image inpainting non-smooth problem show acceleration convex optimization problem
