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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
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1569-3945
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Volume 24, Issue 2

Issues

Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives

Vladimir V. Vasin
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  • Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya St. 16, 620990 Yekaterinburg; and Ural Federal University, Lenin Ave. 51, 620000 Yekaterinburg, Russia
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Published Online: 2015-11-05 | DOI: https://doi.org/10.1515/jiip-2015-0050

Abstract

Under the assumption that the solution of a linear operator equation is presented in the form of a sum of several components with various smoothness properties, a modified Tikhonov regularization method is studied. The stabilizer of this method is the sum of three functionals, where each one corresponds to only one component. Each such functional is either the total variation of a function or the total variation of its derivative. For every component, the convergence of approximate solutions in a corresponding normed space is proved and a general discrete approximation scheme for the regularizing algorithm is justified.

Keywords: Ill-posed problem; total variation; non-smooth solution; finite-difference approximation

MSC: 65J10; 65J20; 65J22

About the article

Received: 2015-05-19

Accepted: 2015-09-19

Published Online: 2015-11-05

Published in Print: 2016-04-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 15-01-00629


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 2, Pages 149–158, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0050.

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