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Nonstationary iterated frozen Tikhonov regularization with uniformly convex penalty terms for solving inverse problems

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  • Mittal, Gaurav

Abstract

In this paper, we propose the frozen form of nonstationary iterated Tikhonov regularization to solve the inverse problems and study its convergence analysis in the Banach space setting, where the iterates of proposed method are defined through minimization problems. These minimization problems involve uniformly convex penalty terms that may be non-smooth, which can be utilized in the reconstruction of several notable features (e.g., discontinuities and sparsity) of the sought solutions. We terminate our method through a discrepancy principle and show its regularizing nature. Moreover, we show the convergence of the iterates of the method with respect to Bregman distance as well as their strong convergence. In order to show the applicability of the proposed method, we show that it is applicable on two ill-posed inverse problems. Finally, by assuming that a stability estimate holds within a certain set, we derive the convergence rates of our method.

Suggested Citation

  • Mittal, Gaurav, 2024. "Nonstationary iterated frozen Tikhonov regularization with uniformly convex penalty terms for solving inverse problems," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    • Handle: RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006884
    DOI: 10.1016/j.amc.2023.128519
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    References listed on IDEAS

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    1. Gaurav Mittal & Ankik Kumar Giri, 2022. "Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 643-680, August.
    2. Mittal, Gaurav & Giri, Ankik Kumar, 2021. "Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. M. Hanke & C. W. Groetsch, 1998. "Nonstationary Iterated Tikhonov Regularization," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 37-53, July.
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