期刊
SIAM JOURNAL ON IMAGING SCIENCES
卷 3, 期 4, 页码 1015-1046出版社
SIAM PUBLICATIONS
DOI: 10.1137/09076934X
关键词
convex optimization; total variation minimization; primal-dual methods; operator splitting; l(1) basis pursuit
类别
资金
- ONR [N00014-03-1-0071]
- NSF [DMS-0610079, CCF-0528583, DMS-0312222]
We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu and Chan in [An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration, CAM Report 08-34, UCLA, Los Angeles, CA, 2008] to a broader class of convex optimization problems. In addition, we survey several closely related methods and explain the connections to PDHG. We point out convergence results for a modified version of PDHG that has a similarly good empirical convergence rate for total variation (TV) minimization problems. We also prove a convergence result for PDHG applied to TV denoising with some restrictions on the PDHG step size parameters. We show how to interpret this special case as a projected averaged gradient method applied to the dual functional. We discuss the range of parameters for which these methods can be shown to converge. We also present some numerical comparisons of these algorithms applied to TV denoising, TV deblurring, and constrained l(1) minimization problems.
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