Open AccessOn Tikhonov-type regularization with approximated penalty terms
Author(s) -
A. Neubauer
Publication year - 2021
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021027
Subject(s) - tikhonov regularization , regularization (linguistics) , mathematics , type (biology) , combinatorics , algorithm , mathematical analysis , inverse problem , computer science , artificial intelligence , ecology , biology
In this paper, we deal with (nonlinear) ill-posed problems that are regularized by minimizing Tikhonov-type functionals. If the minimization is tedious for some penalty term \begin{document}$ P_0 $\end{document} , we approximate it by a family of penalty terms \begin{document}$ ({P_\beta}) $\end{document} having nicer properties and analyze what happens as \begin{document}$ \beta\to 0 $\end{document} . We investigate the discrepancy principle for the choice of the regularization parameter and apply all results to linear problems with sparsity constraints. Numerical results show that the proposed method yields good results.