Array imaging of localized objects in homogeneous and heterogeneous media

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Show simple item record Chai, Anwei Moscoso Castro, Miguel Ángel Papanicolaou, George 2021-04-08T08:10:48Z 2021-04-08T08:10:48Z 2016-10
dc.identifier.bibliographicCitation Chai, A., Moscoso, M. & Papanicolaou, G. (2016). Array imaging of localized objects in homogeneous and heterogeneous media. Inverse Problems, 32(10), 104003.
dc.identifier.issn 0266-5611
dc.description.abstract We 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.
dc.format.extent 32
dc.language.iso eng
dc.publisher IOP Science
dc.rights © 2016 IOP Publishing Ltd
dc.subject.other Array Imaging
dc.subject.other Multiple Scattering
dc.subject.other Random Media
dc.subject.other Sparse Promoting Optimization
dc.subject.other Statistical Stability
dc.title Array imaging of localized objects in homogeneous and heterogeneous media
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 10
dc.identifier.publicationlastpage 32
dc.identifier.publicationtitle Inverse Problems
dc.identifier.publicationvolume 32
dc.identifier.uxxi AR/0000019178
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