Linear and Nonlinear Inverse Scattering Applied to Experimental Data

In this paper, we present our recent work on the imaging techniques for solving the 2–D inverse scattering problems in the frequency and time domain, which is the continuation of our work described in [1]. Two linear algorithms, Synthetic Aperture Focusing Technique (SAFT) and MUltiple SIgnal Classification (MUSIC) algorithm, as well as two nonlinear algorithms, Contrast Source Inversion (CSI) and Multiplicative Regularization Contrast Source Inversion (MR-CSI), are applied to reconstruct the experimental electromagnetic data sets from Institute Fresnel [2], France, and experimental elastic data sets from the Fraunhofer Institute for Non-Destructive Testing (IZFP), Germany. 1. Overview of the Applied Inversion Algorithms In 2–D, the acoustic case, the electromagnetic transversal magnetic (TM) case, and the elastodynamic horizontally polarized shear (SH) case can be treated as scalar cases. Beside that, the transversal electric (TE) case of electromagnetic waves and the pressure and vertically polarized shear (P–SV) case of elastic waves must be treated as vector cases. Throughout this paper we focus on both cases, the scalar and vector case. Details can be found in [3]. Before we introduce the inverse scattering algorithms, we represent the data and object equations for the 2-D scalar, the TE, and P-SV case. We consider a domain D with homogeneous background and inhomogeneous scatterer. The data are measured on the surface M which encloses the domain D. The data and object equations for the 2-D scalar case are