We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two integral equations. This system can be solved numerically by a recently developed spectral method for the direct scattering problem.

A review of some of the author’s results in the area of inverse scattering is given. The following topics are discussed: 1) Property C and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3) Inverse scattering with ”incomplete“ data, 4) Inverse scattering for inhomogeneous Schrödinger equation, 5) Krein’s inverse scattering method, 6) Invertibility of...

Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an eecient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear th...

We consider an inverse problem for the scattering of an obliquely incident electromagnetic wave by an impedance cylinder. In previous work, we have shown that the direct scattering problem is governed by a pair of Helmholtz equations subject to coupled oblique boundary conditions, where the wave number depends on the frequency and the incident angle with respect to the axis of the cylinder. In ...

The Schur algorithm and its times-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propaga...

Abstract—This paper reports a two-dimensional time-domain inverse scattering algorithm based upon the finite-difference time domain method for determining the shape of a perfectly conducting cylinder. Finite difference time domain method (FDTD) is used to solve the scattering electromagnetic wave of a perfectly conducting cylinder. The inverse problem is resolved by an optimization approach and...

We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall discuss the linear sampling method for solving the inverse scattering problem which does not requi...

A matrix Riemann-Hilbert problem associated with the one-dimensional SchrBdinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this Riemann-Hilbert problem yields the solution of the inverse scattering problem for a larger class of potentials than the usual Faddeev class. Some examples of explicit solutions of the Riemann-Hilbert problem ...