Name
Title | ||
|---|---|---|
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/09076934X | SIAM J. Imaging Sciences |
Keywords | DocType | Volume |
first order primal-dual algorithms,tv deblurring,primal-dual hybrid gradient,tv denoising,imaging science,minimization problem,convex optimization,pdhg step size parameter,general framework,efficient primal-dual hybrid gradient,convergence result,gradient method,cam report,good empirical convergence rate,first order | Journal | 3 |
Issue | ISSN | Citations |
4 | 1936-4954 | 185 |
PageRank | References | Authors |
6.41 | 22 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ernie Esser | 1 | 286 | 10.74 |
| Xiaoqun Zhang | 2 | 684 | 29.21 |
| Tony F. Chan | 3 | 8733 | 659.77 |