 Nonstationary iterated frozen Tikhonov regularization with uniformly convex penalty terms for solving inverse problemsGaurav Mittal Applied Mathematics and Computation, 2024, vol. 468, issue C 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. Keywords: Nonlinear ill-posed operator equations; Regularization; Tikhonov-regularization; Iterative regularization methods; Convergence analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006884 DOI: 10.1016/j.amc.2023.128519 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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