Open AccessConvergence of regularization methods with filter functions for a regularization parameter chosen with GSURE
Author(s) -
Bruno Sixou
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1476/1/012011
Subject(s) - regularization (linguistics) , backus–gilbert method , smoothness , regularization perspectives on support vector machines , rate of convergence , mathematics , inverse problem , inverse , mathematical optimization , mathematical analysis , tikhonov regularization , computer science , artificial intelligence , geometry , computer network , channel (broadcasting)
In this work, we show that the regularization methods based on filter functions with a regularization parameter chosen with the GSURE principle are convergent for mildly ill-posed inverse problems and under some smoothness source condition. The convergence rate of the methods is not optimal but the efficiency increases with the smoothness of the solution.