Novel Sampling Methods for Electromagnetic Inverse Scattering Theory

Kansas State University, Manhattan KS

Investigators

Abstract

The inverse electromagnetic scattering problem (IESP) aims to determine an unknown object from the electromagnetic fields scattered by that object. The IESP has been an active research topic in the engineering, mathematics, and physics communities for the past three decades due to its impact on a wide range of applications including radar, nondestructive testing, medical imaging, and geophysical exploration. However, solving the IESP is very challenging since this problem is in general highly nonlinear and severely ill-posed. Therefore, although computational algorithms have been extensively studied for the IESP, there is still a high demand for algorithms with improved efficiency and robustness. The project addresses this demand by developing new and highly efficient sampling-type algorithms for the IESP in the context of optics and radar. This project will also involve the training of undergraduate and graduate students in computational mathematics. Solving the IESP involves proper sampling methods to construct an approximate indicator function for the unknown scattering object. Ideally these sampling methods are fast, non-iterative, and do not require a priori information about the scattering object. In this project, the principal investigator and graduate students will develop new sampling-type methods for the IESP for both the Helmholtz equation and the system of Maxwell's equations in different types of scattering media, including infinite periodic media, small and point-like objects, bounded inhomogeneous media, and nonlinear media. In addition to the aforementioned features, the sampling-type methods that will be developed in this project will be simple to implement and extremely robust against noise in the data. The resolution and stability analysis of these sampling-type methods and their validation by experimental data will be investigated. The new methods are expected to provide a promising alternative tool to solve the IESP in optics and radar. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.