An inexact primal-dual method with correction step for a saddle point problem in image debluring
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916665232457728 |
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| author | Fang, Changjie Hu, Liliang Chen, Shenglan |
| author_facet | Fang, Changjie Hu, Liliang Chen, Shenglan |
| contents | In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix
$D$. Relaxing requirement on primal-dual step sizes, we prove the convergence of the proposed method. We also establish the $O(1/N)$ convergence rate of our method in the ergodic sense. Moreover, we apply our method to solve TV-L$_1$ image deblurring problems. Numerical simulation results illustrate the efficiency of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_00389 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An inexact primal-dual method with correction step for a saddle point problem in image debluring Fang, Changjie Hu, Liliang Chen, Shenglan Optimization and Control In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix $D$. Relaxing requirement on primal-dual step sizes, we prove the convergence of the proposed method. We also establish the $O(1/N)$ convergence rate of our method in the ergodic sense. Moreover, we apply our method to solve TV-L$_1$ image deblurring problems. Numerical simulation results illustrate the efficiency of our method. |
| title | An inexact primal-dual method with correction step for a saddle point problem in image debluring |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2112.00389 |