| Authors |
A. Chambolle, Pock Thomas |
| Appeared in |
Journal of Mathematical Imaging and Vision
|
| Pages |
to appear |
| Date |
2011 |
| Abstract |
In this paper we study a first-order primal-dual algorithm for convex
optimization problems with known saddle-point structure. We prove con-
vergence 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/eN ) on problems where both are uniformly convex. The wide ap-
plicability of the proposed algorithm is demonstrated on several imaging
problems such as image denoising, image deconvolution, image inpainting,
motion estimation and image segmentation.
|
| Link |
URL
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