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Joint additive Kullback–Leibler residual minimization and regularization for linear inverse problems
Author(s) -
Resmerita Elena,
Anderssen Robert S.
Publication year - 2007
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.855
Subject(s) - mathematics , regularization (linguistics) , backus–gilbert method , uniqueness , inverse problem , residual , minification , regularization perspectives on support vector machines , a priori and a posteriori , inverse , mathematical optimization , convergence (economics) , mathematical analysis , algorithm , computer science , tikhonov regularization , philosophy , geometry , epistemology , artificial intelligence , economics , economic growth
For the approximate solution of ill‐posed inverse problems, the formulation of a regularization functional involves two separate decisions: the choice of the residual minimizer and the choice of the regularizor. In this paper, the Kullback–Leibler functional is used for both. The resulting regularization method can solve problems for which the operator and the observational data are positive along with the solution, as occur in many inverse problem applications. Here, existence, uniqueness, convergence and stability for the regularization approximations are established under quite natural regularity conditions. Convergence rates are obtained by using an a priori strategy. Copyright © 2007 John Wiley & Sons, Ltd.