Computing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomography

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dc.contributor.authorO'Connell, Meghanen
dc.contributor.authorKilmer, Misha E.en
dc.contributor.authorde Sturler, Ericen
dc.contributor.authorGugercin, Serkanen
dc.contributor.departmentMathematicsen
dc.date.accessioned2018-01-25T17:21:27Zen
dc.date.available2018-01-25T17:21:27Zen
dc.date.issued2017-01-01en
dc.description.abstractIn nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of the optimization process. In the context of absorption imaging in diffuse optical tomography, one approach to addressing this bottleneck proposed recently (de Sturler, et al, 2015) reformulates the viewing of the forward problem as a differential algebraic system, and then employs model order reduction (MOR). However, the construction of the reduced model requires the solution of several full order problems (i.e. the full discretized PDE for multiple right-hand sides) to generate a candidate global basis. This step is then followed by a rank-revealing factorization of the matrix containing the candidate basis in order to compress the basis to a size suitable for constructing the reduced transfer function. The present paper addresses the costs associated with the global basis approximation in two ways. First, we use the structure of the matrix to rewrite the full order transfer function, and corresponding derivatives, such that the full order systems to be solved are symmetric (positive definite in the zero frequency case). Then we apply MOR to the new formulation of the problem. Second, we give an approach to computing the global basis approximation dynamically as the full order systems are solved. In this phase, only the incrementally new, relevant information is added to the existing global basis, and redundant information is not computed. This new approach is achieved by an inner-outer Krylov recycling approach which has potential use in other applications as well. We show the value of the new approach to approximate global basis computation on two DOT absorption image reconstruction problems.en
dc.description.versionPublished versionen
dc.format.extentB272 - B297 (26) page(s)en
dc.identifier.doihttps://doi.org/10.1137/16M1062880en
dc.identifier.eissn1095-7197en
dc.identifier.issn1064-8275en
dc.identifier.issue2en
dc.identifier.urihttp://hdl.handle.net/10919/81924en
dc.identifier.volume39en
dc.languageEnglishen
dc.publisherSiam Publicationsen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000401776100003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematics, Applieden
dc.subjectMathematicsen
dc.subjectKrylov recyclingen
dc.subjectdiffuse optical tomographyen
dc.subjectmodel order reductionen
dc.subjectnonlinear inverse problemen
dc.subjectINTERPOLATORY PROJECTION METHODSen
dc.subjectINVERSE PROBLEMSen
dc.subjectSHAPE OPTIMIZATIONen
dc.subjectREDUCTIONen
dc.subjectSYSTEMSen
dc.subjectDECOMPOSITIONen
dc.titleComputing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomographyen
dc.title.serialSIAM Journal on Scientific Computingen
dc.typeArticle - Refereeden
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen

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