A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

Christian Clason, Bangti Jin

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Original languageEnglish (US)
Pages (from-to)505-536
Number of pages32
JournalSIAM Journal on Imaging Sciences
Volume5
Issue number2
DOIs
StatePublished - Jan 2012
Externally publishedYes

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