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 illposed 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 illposedness of the electromagnetic imaging problem using sparsitybased 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) Sparsityregularized 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) Sparsityregularized 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) Sparsityregularized 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 threedimensional 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 sparsityregularized 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.
Date of Award  Mar 2016 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Sciences and Engineering


Supervisor  Hakan Bagci (Supervisor) 

 Sparse reconstruction
 Inverse scattering
 Electromagnetic (EM) imaging
 Nonlinear optimization
 Linear Optimization
 Reqularization