A Fast Inverse Scattering Imaging Method by Applying Virtual Experiments to T-Matrix Scheme

Singular matrix Darboux transformations in the inverse-scattering method

Singular Darboux transformations, in contrast to the conventional ones, have a singular matrix as a coefficient before the derivative. We incorporated such transformations into a chain of conventional transformations and presented determinant formulas for the resulting action of the chain. A determinant representation of the Kohlhoff–von Geramb solution to the Marchenko equation is given. PACS ...

Inverse Scattering and Imaging

T-matrix method and its applications to electromagnetic scattering by particles: A current perspective

This note serves as a short introduction to the reprint of our article ‘‘T-matrix computations of light scattering by nonspherical particles: a review’’ (JQSRT 1996; 55:535–75). We first discuss the motivation for writing that article and explain its historical context. This is followed by a short overview of more recent developments. Published by Elsevier Ltd. Although the T-matrix method was ...

Inverse Scattering by the Stability Index Method

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can re...

Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

A novel continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation, which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field. The boundary data is assumed to be available at multiple frequencies. Initial guesses are chosen from a direct imaging algorithm, multiple signal classification (MUSI...