A fast iterative regularization method for ill-posed problems

Ill-posed problems manifest in a wide range of scientific and engineering disciplines. The solutions to these problems exhibit a high degree of sensitivity to data perturbations. Regularization methods strive to alleviate the sensitivity exhibited by these solutions. This paper presents a fast itera...

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Bibliographic Details
Published in:Calcolo Vol. 62; no. 1; p. 1
Main Author: Bechouat, Tahar
Format: Journal Article
Language:English
Published: Milano Springer Nature B.V 01.03.2025
Subjects:
Hilbert space
Ill posed problems
Iterative methods
Principles
Regularization
Regularization methods
Sensitivity
ISSN:0008-0624, 1126-5434
Online Access:Get full text
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Summary:Ill-posed problems manifest in a wide range of scientific and engineering disciplines. The solutions to these problems exhibit a high degree of sensitivity to data perturbations. Regularization methods strive to alleviate the sensitivity exhibited by these solutions. This paper presents a fast iterative scheme for addressing linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization. Both the a-priori and a-posteriori choice rules for regularization parameters are provided, and both rules yield error estimates that are order optimal. In comparison to the nonstationary iterated Tikhonov method, the newly introduced method significantly reduces the required number of iterations to achieve convergence based on an appropriate stopping criterion. The numerical computations provide compelling evidence regarding the efficacy of our new iterative regularization method. Furthermore, the versatility of this method extends to image restorations.
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ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-024-00626-9