Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives / Vasin Vladimir V. // JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - 2016. - V. 24, l. 2. - P. 149-158.

ISSN/EISSN:

0928-0219 / 1569-3945

Type:

Article; Proceedings Paper

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.

Author keywords:

Ill-posed problem; total variation; non-smooth solution; finite-difference approximation RECONSTRUCTION; APPROXIMATION; SINGULARITIES; COMPONENTS; OPERATORS; SMOOTH

DOI:

10.1515/jiip-2015-0050

Web of Science ID:

ISI:000373528700006

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Note	7th International Conference on Inverse Problems - Modeling and Simulation, Oludeniz, TURKEY, MAY 26-31, 2014
Publisher	WALTER DE GRUYTER GMBH
Address	GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Language	English
EISSN	1569-3945
Keywords-Plus	RECONSTRUCTION; APPROXIMATION; SINGULARITIES; COMPONENTS; OPERATORS; SMOOTH
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vasin@imm.uran.ru
Number-of-Cited-References	23
Usage-Count-Since-2013	3
Journal-ISO	J. Inverse Ill-Posed Probl.
Doc-Delivery-Number	DI5HE