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Error Estimations for Total Variation Type Regularization

Author

Listed:
  • Kuan Li

    (School of Cyberspace Security, Dongguan University of Technology, Dongguan 523808, China
    Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen 518060, China)

  • Chun Huang

    (College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China)

  • Ziyang Yuan

    (Department of Mathematics, National University of Defense Technology, Changsha 410073, China)

Abstract

This paper provides several error estimations for total variation (TV) type regularization, which arises in a series of areas, for instance, signal and imaging processing, machine learning, etc. In this paper, some basic properties of the minimizer for the TV regularization problem such as stability, consistency and convergence rate are fully investigated. Both a priori and a posteriori rules are considered in this paper. Furthermore, an improved convergence rate is given based on the sparsity assumption. The problem under the condition of non-sparsity, which is common in practice, is also discussed; the results of the corresponding convergence rate are also presented under certain mild conditions.

Suggested Citation

  • Kuan Li & Chun Huang & Ziyang Yuan, 2021. "Error Estimations for Total Variation Type Regularization," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1373-:d:574477
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    References listed on IDEAS

    as
    1. Ding, Meng & Huang, Ting-Zhu & Wang, Si & Mei, Jin-Jin & Zhao, Xi-Le, 2019. "Total variation with overlapping group sparsity for deblurring images under Cauchy noise," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 128-147.
    2. Chenxi Chen & Yunmei Chen & Yuyuan Ouyang & Eduardo Pasiliao, 2018. "Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 676-695, November.
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