Solving the PEC Inverse Scattering Problem with A Linear Model

Abstract

In this paper, the nonlinear perfect electric conductor (PEC) inverse scattering problem was addressed with a linear model. First, finite difference frequency domain (FDFD) was used to discretize the problem. Then, the contrast and the total field were included into the contrast source to formulate a linear model. Due to the fact that the induced current only exists
on the surface of the PEC scatterers, reconstruction methods in compressive sensing (CS) can be used to recover the contrast source which is able to indicate the shape of the PEC objects. To further enhance the inversion performance, the multiple measurement vector (MMV) model was used to exploit the joint sparsity of the contrast sources corresponding to different incident angles. This method shares some common merits with other inversion methods: First, it does not require a priori information on the position and quantity of the scatterers. Second, nonconvex PEC objects can be successfully reconstructed. Third, it enables simple incorporation with complicated background media without increasing extra computational burden. In addition, it also shows its own advantages that cannot be achieved in other inversion methods: First, it solves the nonlinear inverse scattering problems based on the vectorial Maxwell equations with a linear model.
Second, the sensing matrix is much less compared to the inverse of the stiffness matrix in FDFD scheme, so it can be computed and stored beforehand to circumvent the matrix inverse computation and achieve fast inversion. Numerical simulation results with the transverse magnetic (TM) data in 2D configuration demonstrated the validity of the proposed method.