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    Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

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    Name:
    Abdulla Desmal__Final Thesis.pdf
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    6.867Mb
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    PDF
    Description:
    Final Dissertation
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    Type
    Dissertation
    Authors
    Desmal, Abdulla cc
    Advisors
    Bagci, Hakan cc
    Committee members
    Al-Naffouri, Tareq Y. cc
    Hoteit, Ibrahim cc
    Moghaddam, Mahta
    Program
    Electrical Engineering
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2016-03
    Permanent link to this record
    http://hdl.handle.net/10754/602275
    
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    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.
    Citation
    Desmal, A. (2016). Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging. KAUST Research Repository. https://doi.org/10.25781/KAUST-7X24F
    DOI
    10.25781/KAUST-7X24F
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-7X24F
    Scopus Count
    Collections
    PhD Dissertations; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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