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2011•Journal of Yunnan University of NationalitiesRequires access

A Case Study of the Regularization Methods for Ill-Posed Inverse Problems

Peng Lihui

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Abstract

Inverse problem,as a branch of mathematics,is associated with the reversal of the cause-effect sequence and consists of finding the unknown causes of known consequences.A case study,which is based on the characterizations of the ill-posedness with inverse problems and the essence behind the regularization method for ill-posed inverse problem solving,is presented in this paper.The Tikhonov regularization method and the Landweber iteration are introduced.The spectral filters for the corresponding regularization methods are also discussed.

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What this paper is about

Inverse problem,as a branch of mathematics,is associated with the reversal of the cause-effect sequence and consists of finding the unknown causes of known consequences.A case study,which is based on the characterizations of the ill-posedness with inverse problems and the essence behind the regularization method for ill-posed inverse problem solving,is presented in this paper.The Tikhonov regularization method and the Landweber iteration are introduced.The spectral filters for the corresponding regularization methods are also discussed.

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Available abstract

Inverse problem,as a branch of mathematics,is associated with the reversal of the cause-effect sequence and consists of finding the unknown causes of known consequences.A case study,which is based on the characterizations of the ill-posedness with inverse problems and the essence behind the regularization method for ill-posed inverse problem solving,is presented in this paper.The Tikhonov regularization method and the Landweber iteration are introduced.The spectral filters for the corresponding regularization methods are also discussed.

Key concepts: Tikhonov regularization, Backus–Gilbert method, Regularization (linguistics), Inverse problem, Well-posed problem, Mathematics, Inverse, Regularization perspectives on support vector machines

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