An Analysis of the Zero-Crossing Method for Choosing Regularisation Parameters

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Author(s)
Johnston, PR
Gulrajani, RM
Griffith University Author(s)
Year published
2002
Metadata
Show full item recordAbstract
Solving discrete ill-posed problems via Tikhonov regularization introduces the problem of determining a regularization parameter. There are several methods available for choosing such a parameter, yet, in general, the uniqueness of this choice is an open question. Two empirical methods for determining a regularization parameter (which appear in the biomedical engineering literature) are the composite residual and smoothing operator and the zero-crossing method. An equivalence is established between the zero-crossing method and a minimum product criterion, which has previously been linked with the L-curve method. Finally, the ...
View more >Solving discrete ill-posed problems via Tikhonov regularization introduces the problem of determining a regularization parameter. There are several methods available for choosing such a parameter, yet, in general, the uniqueness of this choice is an open question. Two empirical methods for determining a regularization parameter (which appear in the biomedical engineering literature) are the composite residual and smoothing operator and the zero-crossing method. An equivalence is established between the zero-crossing method and a minimum product criterion, which has previously been linked with the L-curve method. Finally, the uniqueness of a choice of regularization parameter is established under certain restrictions on the Fourier coefficients of the data in the ill-posed problem.
View less >
View more >Solving discrete ill-posed problems via Tikhonov regularization introduces the problem of determining a regularization parameter. There are several methods available for choosing such a parameter, yet, in general, the uniqueness of this choice is an open question. Two empirical methods for determining a regularization parameter (which appear in the biomedical engineering literature) are the composite residual and smoothing operator and the zero-crossing method. An equivalence is established between the zero-crossing method and a minimum product criterion, which has previously been linked with the L-curve method. Finally, the uniqueness of a choice of regularization parameter is established under certain restrictions on the Fourier coefficients of the data in the ill-posed problem.
View less >
Journal Title
SIAM Journal on Scientific Computing
Volume
24
Issue
2
Publisher URI
Copyright Statement
© 2002 SIAM. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Subject
Applied mathematics
Numerical and computational mathematics
Theory of computation