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dc.contributor.authorBardsley, Johnathan M.
dc.contributor.authorSolonen, Antti
dc.contributor.authorCui, Tiangang
dc.contributor.authorWang, Zheng
dc.contributor.authorMarzouk, Youssef M
dc.date.accessioned2018-04-09T16:05:45Z
dc.date.available2018-04-09T16:05:45Z
dc.date.issued2017-01
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/1721.1/114625
dc.description.abstractPrior distributions for Bayesian inference that rely on the L[subscript 1]-norm of the parameters are of considerable interest, in part because they promote parameter fields with less regularity than Gaussian priors (e.g., discontinuities and blockiness). These L[subscript 1]-type priors include the total variation (TV) prior and the Besov space B[subscript 1,1][superscript s] prior, and in general yield non-Gaussian posterior distributions. Sampling from these posteriors is challenging, particularly in the inverse problem setting where the parameter space is high-dimensional and the forward problem may be nonlinear. This paper extends the randomize-then-optimize (RTO) method, an optimization-based sampling algorithm developed for Bayesian inverse problems with Gaussian priors, to inverse problems with L[subscript 1]-type priors. We use a variable transformation to convert an L[subscript 1]-type prior to a standard Gaussian prior, such that the posterior distribution of the transformed parameters is amenable to Metropolized sampling via RTO. We demonstrate this approach on several deconvolution problems and an elliptic PDE inverse problem, using TV or Besov space B[subscript 1,1][superscript s] priors. Our results show that the transformed RTO algorithm characterizes the correct posterior distribution and can be more efficient than other sampling algorithms. The variable transformation can also be extended to other non-Gaussian priors. (An erratum is attached.)en_US
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/16M1080938en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleBayesian Inverse Problems with L[subscript 1] Priors: A Randomize-Then-Optimize Approachen_US
dc.typeArticleen_US
dc.identifier.citationWang, Zheng, Johnathan M. Bardsley, Antti Solonen, Tiangang Cui, and Youssef M. Marzouk. “Bayesian Inverse Problems with L[subscript 1] Priors: A Randomize-Then-Optimize Approach.” SIAM Journal on Scientific Computing 39, 5 (January 2017): S140–S166 © 2017 Society for Industrial and Applied Mathematicsen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.contributor.mitauthorWang, Zheng
dc.contributor.mitauthorMarzouk, Youssef M
dc.relation.journalSIAM Journal on Scientific Computingen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2018-04-04T15:58:38Z
dspace.orderedauthorsWang, Zheng; Bardsley, Johnathan M.; Solonen, Antti; Cui, Tiangang; Marzouk, Youssef M.en_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-4478-2468
dc.identifier.orcidhttps://orcid.org/0000-0001-8242-3290
mit.licenseOPEN_ACCESS_POLICYen_US


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