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

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Johnston, PR
Gulrajani, RM
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2002
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Abstract

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.

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SIAM Journal on Scientific Computing

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24

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2

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© 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.

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Applied mathematics

Numerical and computational mathematics

Theory of computation

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