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Array imaging of localized objects in homogeneous and heterogeneous media

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Métodos Numéricos y Aplicacioneses
dc.affiliation.institutoUC3M. Instituto Universitario sobre Modelización y Simulación en Fluidodinámica, Nanociencia y Matemática Industrial Gregorio Millán Barbanyes
dc.contributor.authorChai, Anwei
dc.contributor.authorMoscoso, Miguel
dc.contributor.authorPapanicolaou, George
dc.date.accessioned2021-04-08T08:10:48Z
dc.date.available2021-04-08T08:10:48Z
dc.date.issued2016-10
dc.description.abstractWe present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and multiple and single scattering situations. When the media is homogeneous with strong multiple scattering between scatterers, we give a non-iterative formulation to find the locations and reflectivities of the scatterers from a nonlinear inverse problem in two steps, using either single or multiple illuminations. We further introduce an approach that uses the top singular vectors of the response matrix as optimal illuminations, which improves the robustness of sparse promoting optimization with respect to additive noise. When multiple scattering is negligible, the optimization problem becomes linear and can be reduced to a hybrid-ℓ1 method when optimal illuminations are used. When the media is random, and the interaction with the unknown inhomogeneities can be primarily modeled by wavefront distortions, we address the statistical stability of these methods. We analyze the fluctuations of the images obtained with the hybrid-ℓ1 method, and we show that it is stable with respect to different realizations of the random medium provided the imaging array is large enough. We compare the performance of the hybrid-ℓ1 method in random media to the widely used Kirchhoff migration and the multiple signal classification methods.en
dc.format.extent32
dc.identifier.bibliographicCitationChai, A., Moscoso, M. & Papanicolaou, G. (2016). Array imaging of localized objects in homogeneous and heterogeneous media. Inverse Problems, 32(10), 104003.en
dc.identifier.doihttps://doi.org/10.1088/0266-5611/32/10/104003
dc.identifier.issn0266-5611
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue10
dc.identifier.publicationlastpage32
dc.identifier.publicationtitleInverse Problemsen
dc.identifier.publicationvolume32
dc.identifier.urihttps://hdl.handle.net/10016/32303
dc.identifier.uxxiAR/0000019178
dc.language.isoengen
dc.publisherIOP Scienceen
dc.rights© 2016 IOP Publishing Ltden
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherArray Imagingen
dc.subject.otherMultiple Scatteringen
dc.subject.otherRandom Mediaen
dc.subject.otherSparse Promoting Optimizationen
dc.subject.otherStatistical Stabilityen
dc.titleArray imaging of localized objects in homogeneous and heterogeneous mediaen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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