Direct Sampling Methods For Inverse Scattering Problems
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DIRECT SAMPLING METHODS FOR INVERSE SCATTERING PROBLEMS
Abstract : Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on Rd, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer. In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, include Multiple Signal Classification (MUSIC) by Devaney, the Linear Sampling Method (LSM) by Colton and Kirsch, the Factorization Method by Kirsch, and the Direct Sampling Method by Ito et al. In Chapter 2, we introduce some direct sampling methods, including Orthogonality Sampling by Potthast and a direct sampling method using far field measurements for shape reconstruction by Liu. In Chapter 3, we generalize Liu's method for shape reconstruction in inverse electromagnetic scattering problems. The method applies in an inhomogeneous isotropic medium in R3 and uses the far field measurements. We study the behavior of the new indicator for the sampling points both outside and inside the scatterer. In Chapter 4, we propose a new sampling method for multifrequency inverse source problem for time-harmonic acoustics using a finite set of far field data. We study the theoretical foundation of the proposed sampling method, and present some numerical experiments to demonstrate the feasibility and effectiveness of the method. Final conclusions of this thesis are summarized in Chapter 5. Recommendations for possible future works are also given in this chapter.
Numerical Methods for Inverse Scattering Problems
This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.
Computational Methods for Electromagnetic Inverse Scattering
A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field