Heuristic parameter selection based on functional minimization: Optimality and model function approach

Heuristic parameter selection based on functional minimization: Optimality and model function approach

We analyze some parameter choice strategies in regularization of inverse problems, in particular, the (modified) L-curve method and a variant of the Hanke-Raus type rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these funct...

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Bibliographic Details
Published in:Mathematics of computation Vol. 82; no. 283; pp. 1609 - 1630
Main Authors: LU, SHUAI, MATHÉ, PETER
Format: Journal Article
Language:English
Published: American Mathematical Society 01-07-2013
Subjects:
Error bounds
Heuristics
Ill posed problems
Inverse problems
Mathematical functions
Mathematical independent variables
Mathematical problems
Mathematical theorems
Modeling
Parametric models
Parameter choice
model function
L-curve
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Summary:We analyze some parameter choice strategies in regularization of inverse problems, in particular, the (modified) L-curve method and a variant of the Hanke-Raus type rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2013-02674-9