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Analysis of the bounded variation and the G regularization for nonlinear inverse problems
Author(s) -
Cimrák I.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1239
Subject(s) - mathematics , regularization (linguistics) , uniqueness , minification , bounded function , inverse problem , norm (philosophy) , nonlinear system , inverse , bounded variation , term (time) , mathematical optimization , mathematical analysis , computer science , geometry , physics , quantum mechanics , artificial intelligence , political science , law
We analyze the energy method for inverse problems. We study the unconstrained minimization of the energy functional consisting of a least‐square fidelity term and two other regularization terms being the seminorm in the BV space and the norm in the G space. We consider a coercive (non)linear operator modelling the forward problem. We establish the uniqueness and stability results for the minimization problems. The stability is studied with respect to the perturbations in the data, in the operator, as well as in the regularization parameters. We settle convergence results for the general minimization schemes. Copyright © 2009 John Wiley & Sons, Ltd.