The inverse scattering problem for the difference operators: The decomposition method

Abstract

Abstract. The inverse scattering problem of determining the boundary impedance from knowledge of the time harmonic incident wave and the far-field pattern of the scattered wave is considered. We solve the finite difference Helmholtz equation subject to the exact radiation condition for the discrete problem. The approach is decomposed into two steps. First, we reduce the problem to a well-posed system of linear equations for a modified potential. We next find the boundary impedance using the modified potential through an explicit formula. Thus, the computational part of the nonlinear problem of reconstruction of the boundary impedance is reduced to the solution of a linear system. Numerical examples are given to demonstrate efficiency of the new method.

On the Combination of SAR and Model Based Techniques for High-Resolution Real-Time Two-Dimensional Reconstruction

“…Other possible approaches are based on the impedance boundary condition [10] or the so-called decomposition methods [11]. Although interesting approaches, these methods still rely on matrix inversions and regularization and do not seem suitable for real time applications.…”