Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

Handle URI:
http://hdl.handle.net/10754/602275
Title:
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
Authors:
Desmal, Abdulla ( 0000-0003-0861-8908 )
Abstract:
Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using synthetically generated or actually measured scattered fields, show that the images recovered by these sparsity-regularized methods are sharper and more accurate than those produced by existing methods. The methods developed in this work have potential application areas ranging from oil/gas reservoir engineering to biological imaging where sparse domains naturally exist.
Advisors:
Bagci, Hakan ( 0000-0002-5232-2349 )
Committee Member:
Al-Naffouri, Tareq Y.; Hoteit, Ibrahim ( 0000-0002-3751-4393 ) ; Moghaddam, Mahta
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program
Program:
Electrical Engineering
Issue Date:
Mar-2016
Type:
Dissertation
Appears in Collections:
Dissertations; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorBagci, Hakanen
dc.contributor.authorDesmal, Abdullaen
dc.date.accessioned2016-03-20T09:21:55Zen
dc.date.available2016-03-20T09:21:55Zen
dc.date.issued2016-03en
dc.identifier.urihttp://hdl.handle.net/10754/602275en
dc.description.abstractElectromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using synthetically generated or actually measured scattered fields, show that the images recovered by these sparsity-regularized methods are sharper and more accurate than those produced by existing methods. The methods developed in this work have potential application areas ranging from oil/gas reservoir engineering to biological imaging where sparse domains naturally exist.en
dc.language.isoenen
dc.subjectSparse reconstructionen
dc.subjectInverse scatteringen
dc.subjectElectromagnetic (EM) imagingen
dc.subjectNonlinear optimizationen
dc.subjectLinear Optimizationen
dc.subjectReqularizationen
dc.titleSparse Reconstruction Schemes for Nonlinear Electromagnetic Imagingen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberAl-Naffouri, Tareq Y.en
dc.contributor.committeememberHoteit, Ibrahimen
dc.contributor.committeememberMoghaddam, Mahtaen
thesis.degree.disciplineElectrical Engineeringen
thesis.degree.nameDoctor of Philosophyen
dc.person.id101919en
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