This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering coefficients and the far-field pattern is also derived. Furthermore, the sensitivity of the scattering coefficients with respect to changes in the permittivity and pe...

Abstract. We study an inverse scattering problem for Maxwell’s equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered returns. The mathematical formulation of the inverse scattering problem is based on the electromagnetic Lippmann-Schwinger integral equation and an exp...

In this article the Marchenko integral equations leading to the solution of the inverse scattering problem for the 1-D Schrödinger equation on the line are solved numerically. The linear system obtained by discretization has a structured matrix which allows one to apply FFT based techniques to solve the inverse scattering problem with minimal computational complexity. The numerical results agre...

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.

A nonlinear reconstruction scheme based on the Distorted Born Iterative Method (DBIM) is presented to solve two-dimensional inverse scattering problems with metallic scatterers. Half-quadratic regularization alleviates the inherently ill-posed problem of nonlinear inverse scattering while simultaneously preserving edges. Reconstruction results are found by minimizing a cost function. A bistatic...

Abstract. By developing the ∂̄-approach to global ”inverse scattering” at zero energy we give a principal effectivization of the global reconstruction method for the Gel’fandCalderon inverse boundary value problem in three dimensions. This work goes back to results published by the author in 1987, 1988 and proceeds from recent progress in the ∂̄-approach to inverse scattering in 3D published by t...

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asy...

In recent years there has been considerable interest in the inverse scattering problem for anisotropic medium, particularly in the case of acoustic waves and electromagnetic waves. Due to the lack of uniqueness in determining the constitutive parameters, traditional methods for solving the inverse scattering problems based on the use of weak scattering approximations or nonlinear optimization t...

Measuring particle size distribution through calculating light scattering intensity is a typical inverse problem. This paper builds an inverse mathematical model based on Mie scattering, deduces the inversion formulas for particle size, and calculates the relative coefficients through programming with built-in functions in MATLAB. In order to improve the accuracy and noise immunity of particle ...