This final chapter introduces an inverse electromagnetic reconstruction problem of finding the shape of a scatterer from far field data. It focuses on the Linear Sampling Method that reduces the problem to the solution of many linear integral equations. Using techniques from earlier in the book as well as reciprocity of the solution, the uniqueness of the solution of the inverse problem is proved. The inverse problem is shown to be ill-posed, but a partial mathematical justification of the inversion scheme is shown. Details of the Morozov discrepancy principle and Tikhonov regularization scheme used to approximate the integral equations are given, and numerical results are provided to illustrate the scheme.
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