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An inexact primal–dual method with correction step for a saddle point problem in image debluring

Author

Listed:
  • Changjie Fang

    (Chongqing University of Posts and Telecommunications
    Chongqing University of Posts and Telecommunications)

  • Liliang Hu

    (Chongqing University of Posts and Telecommunications
    Chongqing University of Posts and Telecommunications)

  • Shenglan Chen

    (Chongqing University of Posts and Telecommunications
    Chongqing University of Posts and Telecommunications)

Abstract

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- $$\hbox {L}_1$$ L 1 image deblurring problems. Numerical simulation results illustrate the efficiency of our method.

Suggested Citation

  • Changjie Fang & Liliang Hu & Shenglan Chen, 2023. "An inexact primal–dual method with correction step for a saddle point problem in image debluring," Journal of Global Optimization, Springer, vol. 87(2), pages 965-988, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01211-6
    DOI: 10.1007/s10898-022-01211-6
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