Linear and nonlinear subsurface inverse scattering algorithms based on the contrast source formulations

This paper deals with the problem of localizing and characterizing cylindrical dielectric objects embedded in a homogeneous half-space from the knowledge of the electromagnetic scattered fields, i.e., the measurement data. We present and compare linear and nonlinear inversion algorithms based on the contrast source formulation. Both inversions are considered as optimization problems in which in each iteration the contrast sources and the material contrast are alternatingly updated by minimizing a cost functional. Further, in order to improve the reconstructed images the weighted L²-norm total variation constraint is used. This constraint has been included as a multiplicative constraint so that there is no need to determine the so-called regularization parameter before the inversion process has been started. The present analysis is restricted to the simpler two-dimensional TM polarization case. However, the procedures can be extended to the three-dimensional general case without any fundamental difficulty.