 Inverse scattering problem

An inverse scattering problem reconstructs a medium or obstacle from measured scattered waves. Under the Born approximation, fixed-frequency far-field data sample the Fourier transform of the scattering potential on a restricted frequency surface.

The inverse scattering problem is a mathematical and physical challenge that involves determining the properties of an object or medium based on the scattered waves that arise when an incident wave interacts with it. This problem is particularly relevant in fields such as physics, engineering, and medical imaging, where the goal is to reconstruct information about an object's shape, composition, or internal structure from the measurements of waves (such as electromagnetic, acoustic, or seismic waves) that are scattered off of it.