Journal article
Comparing parameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation, Vol.81(9), pp.1795-1841
2011
Abstract
In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluates and compares them in a large simulation study for spectral cut-off and Tikhonov regularization. The test cases cover a wide range of linear inverse problems with both white and colored stochastic noise. The results show some marked differences between the methods, in particular, in their stability with respect to the noise and its type. We conclude with a table of properties of the methods and a summary of the simulation results, from which we identify the best methods.
Details
- Title
- Comparing parameter choice methods for regularization of ill-posed problems
- Authors/Creators
- F. Bauer (Author/Creator)M.A. Lukas (Author/Creator)
- Publication Details
- Mathematics and Computers in Simulation, Vol.81(9), pp.1795-1841
- Publisher
- Elsevier B.V.
- Identifiers
- 991005541605507891
- Copyright
- © 2011 IMACS.
- Murdoch Affiliation
- School of Chemical and Mathematical Science
- Language
- English
- Resource Type
- Journal article
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- Domestic collaboration
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- Citation topics
- 9 Mathematics
- 9.162 Numerical Methods
- 9.162.1492 Inverse Problems
- Web Of Science research areas
- Computer Science, Interdisciplinary Applications
- Computer Science, Software Engineering
- Mathematics, Applied
- ESI research areas
- Engineering