Inverse Scattering Source Problems

Abstract

The purpose of this chapter is to discuss some of the highlights of the mathematical theory of direct and inverse scattering and inverse source scattering problem for acoustic, elastic and electromagnetic waves. We also briefly explain the uniqueness of the external source for acoustic, elastic and electromagnetic waves equation. However, we must first issue a caveat to the reader. We will also present the recent results for inverse source problems. The resents results including a logarithmic estimate consists of two parts: the Lipschitz part data discrepancy and the high frequency tail of the source function. In general, it is known that due to the existence of non-radiation source, there is no uniqueness for the inverse source problems at a fixed frequency.

Revealing the Invisible: Imaging Through Non-Radiating Subspace

“…Inverse problems in electromagnetics, encompassing inverse source [1,2], inverse scattering [3][4][5][6], inverse design [7], and inverse synthesis [8] problems, have found widespread applications in various fields, including microwave imaging [9], radar tracking [10], breast cancer detecting [11], remote sensing [12], tomography [13], seismology [14], failure analysis [15], nondestructive evaluation [16], antenna design and pattern synthesis [17,18], nanoscale optical positioning [19], and integrated quantum photonics [20][21][22]. Among these, electromagnetic inverse scattering focuses on detecting, locating, shape finding, and material imaging of unknown objects using scattered fields and Maxwell's equations.…”