Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 81, Issue 9, Pages 1795-1841Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2011.01.016
Keywords
Ill-posed problem; Inverse problem; Regularization parameter; Spectral cut-off regularization; Tikhonov regularization
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Funding
- University of Gottingen [1023]
- Upper Austrian Technology and Research Promotion
- University of Linz
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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. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.
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