We are concerned with fast methods for the numerical implementation of the direct and inverse scattering problems for a perfectly conducting obstacle. The scattering problem is usually reduced to a single uniquely solvable modified combined-field integral equation (MCFIE). For the numerical solution of the M-CFIE we propose a new high-order spectral algorithm by transporting this equation on th...

The assumption of weak scattering is standard for the mathematical analysis of synthetic aperture radar (SAR), as it helps linearize the inverse problem via the first Born approximation and thus makes it amenable to solution. Yet it is not consistent with another common assumption, that the interrogating waves do not penetrate into the target material and get scattered off its surface only, whi...

We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. In [S. Kusiak and J. Sylvester, Comm. Pure Appl. Math., 56 (2003), pp. 1525–1548], we introduced the convex scattering support of a far field, a set which will be a subset of the convex hull of the support of any source ...

In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...

Ultrasonic Computed Tomography (UCT) is a full digital imaging technique, which consists in numerically solving the inverse scattering problem associated to the forward scattering problem describing the interaction of ultrasonic waves with inhomogeneous media. For weakly inhomogeneous media such as soft tissues, various approximations of the solution of the forward problem (straight ray approxi...

The inverse problem under consideration is to reconstruct the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from the far field pattern for scattering of time-harmonic acoustic or E-polarized electromagnetic plane waves. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman [10] for the case of the inverse...

In an inverse scattering problem, the fields in the inhomogeneous wave equation are known, and it is desired to solve for the source term. N. N. Bojarski has recently derived an Exact Inverse Scattering Theory for such "inverse source" problems. The problem of determining the generalized refractive index (i.e., the complex permeability and dielectric constant for an electromagnetic problem, or ...

In this paper we discuss one dimensional scattering and inverse scattering for the Helmholtz equation on the half line from the point of view of the layer stripping. By full or nonlinear scattering, we mean the transformation between the index of refraction (actually half of its logarithmic derivative) and the reflection coefficient. We refer to this mapping as nonlinear scattering, because the...

This paper addresses the scattering of acoustic and electromagnetic waves from a permrbed dissipative half-space. For simplicily, the perturbation is assumed to have compact support. Section 1 discusses the application that motivated this work and explains how the scalar model used here is related to Maxwell's equations. Section 2 introduces three formulations for direct and inverse problems fo...