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 language | English (US) |
|---|---|
| Pages (from-to) | 505-536 |
| Number of pages | 32 |
| Journal | SIAM Journal on Imaging Sciences |
| Volume | 5 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.