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

Type
Article

Authors
Clason, Christian
Jin, Bangti

KAUST Grant Number
KUS-C1-016-04

Date
2012-01

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.

Citation
Clason C, Jin B (2012) A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise. SIAM Journal on Imaging Sciences 5: 505–536. Available: http://dx.doi.org/10.1137/110826187.

Acknowledgements
This author’s work was supported by the Austrian Science Fund (FWF) under grantSFB F32 (SFB “Mathematical Optimization and Applications in Biomedical Sciences”).This author’s work was supported by AwardKUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM Journal on Imaging Sciences

DOI
10.1137/110826187

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