Iterative Nonlinear Reconstruction of Isotropic and Anisotropic 2d Objects Using Te and Tm Polarizations

The characterization of buried or non-buried objects generally constitutes an increasingly wide area of research with various applications. In this paper, we present a 2D microwave imaging algorithm taking into account both 2D-TM and 2D-TE polarization configurations. The development of a forward scattering algorithm is first described. Second, the inverse problem is obtained by minimizing a cost function with a Bi-Conjugate method. An edge preserving regularization technique is added to improve the accuracy of the reconstructed images. Several configurations of reconstructions with homogeneous, isotropic and anisotropic objects illustrate the capabilities of the method. INTRODUCTION Algorithms using in microwave imaging are generally developed for 2D-TM polarization (electric field perpendicular to the cross-section of the object) but rarely in 2D-TE (electric field parallel with the cross section of the objects). That can be explained as this configuration leads to more complex calculations and expensive computation times [1]. Many studies have been presented in quantitative microwave imaging using moment method Point Matching and pulse basis functions, but there were only fitted to objects presenting a low dielectric contrast with the background medium [2]. In the 90s appeared techniques that explained the limitations resulting from the forward problem [2]. The solution of the forward problem needs the use of more adapted basis functions leading to more complex calculations [1], [3]. FORWARD SCATTERING PROBLEM In order to develop an imaging algorithm for both 2D-TM and 2D-TE polarizations, we start with the following integro-differential representation of the electric field for the forward scattering problem: ( ) ( ) [ ] E E k G E TOT INC ext TOT = + + ∇∇ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ∗ 0 2 0 ε ε χ ρ . where E and E are the total and incident electric field, respectively, k 0 2 2 0 0 = ω ε μ , εext the permittivity of the background medium, G the Green’s function and χ(ρ) the dielectric contrast of the scatterer, that is assumed here to be a diagonal tensor: