Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems

Application of the Inhomogeneous Lippmann-Schwinger Equation to Inverse Scattering Problems

Abstract. In this paper we present a hybrid approach to numerically solving two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is “hybrid” in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion...

Inverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension.

The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...

The Operator Equations of Lippmann-Schwinger Type for Acoustic and Electromagnetic Scattering Problems in L

This paper is concerned with the scattering of acoustic and electromagnetic time harmonic plane waves by an inhomogeneous medium. These problems can be translated into volume integral equations of the second kind – the most prominent example is the Lippmann-Schwinger integral equation. In this work, we study a particular class of scattering problems where the integral operator in the correspond...

Sparsifying Preconditioner for the Lippmann-Schwinger Equation

The Lippmann–Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous medium and quantum scattering from a localized potential. We present the sparsifying preconditioner for accelerating the iterative solution of the Lippmann–Schwinger equation. This new preconditioner transforms the discretized Lippmann–Schwinger equation into spa...

A parallel radial bisection algorithm for inverse scattering problems