Topological methods offer a rigorous mathematical framework that underpins modern approaches to inverse scattering and imaging. By quantifying the sensitivity of a misfit or cost functional to ...

Vol. 19, No. 3, Special Issue: Integral Equations and Inverse Boundary Value Problems (FALL 2007), pp. 237-260 (24 pages) We study the inverse problem to reconstruct the shape of a three dimensional ...

Recent advances at the intersection of neural networks and inverse scattering problems have transformed traditional approaches to imaging and material characterisation. Inverse scattering involves ...

The "elliptic" version of a three-dimensional nonlinear integrable equation, the Toda chain equation, is studied by means of the inverse scattering method. Several classes of decaying solutions ...