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dc.contributor.authorClason, Christian
dc.contributor.authorJin, Bangti
dc.date.accessioned2016-02-25T12:32:31Z
dc.date.available2016-02-25T12:32:31Z
dc.date.issued2012-01
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.
dc.identifier.issn1936-4954
dc.identifier.doi10.1137/110826187
dc.identifier.urihttp://hdl.handle.net/10754/597404
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.
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).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectImpulsive noise
dc.subjectL1 data fitting
dc.subjectNoise model
dc.subjectParameter identification
dc.subjectRegularization parameter
dc.subjectSemismooth Newton method
dc.titleA Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
dc.typeArticle
dc.identifier.journalSIAM Journal on Imaging Sciences
dc.contributor.institutionKarl-Franzens-Universitat Graz, Graz, Austria
dc.contributor.institutionTexas A and M University, College Station, United States
kaust.grant.numberKUS-C1-016-04


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