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

Handle URI:
http://hdl.handle.net/10754/597404
Title:
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Authors:
Clason, Christian; Jin, Bangti
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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Imaging Sciences
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2012
DOI:
10.1137/110826187
Type:
Article
ISSN:
1936-4954
Sponsors:
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).
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Full metadata record

DC FieldValue Language
dc.contributor.authorClason, Christianen
dc.contributor.authorJin, Bangtien
dc.date.accessioned2016-02-25T12:32:31Zen
dc.date.available2016-02-25T12:32:31Zen
dc.date.issued2012-01en
dc.identifier.citationClason 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.en
dc.identifier.issn1936-4954en
dc.identifier.doi10.1137/110826187en
dc.identifier.urihttp://hdl.handle.net/10754/597404en
dc.description.abstractThis 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.en
dc.description.sponsorshipThis 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).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectImpulsive noiseen
dc.subjectL1 data fittingen
dc.subjectNoise modelen
dc.subjectParameter identificationen
dc.subjectRegularization parameteren
dc.subjectSemismooth Newton methoden
dc.titleA Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noiseen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Imaging Sciencesen
dc.contributor.institutionKarl-Franzens-Universitat Graz, Graz, Austriaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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