The PI will develop analytical and computational tools for inverse scattering problems.
Abstract
Project Abstract In this project, numerical methods for 3-dimenisonal Inverse Scattering Problems without the phase information will be developed analytically and implemented computationally. Only the modulus of the complex valued scattering wave field will be assumed to be known. The phase will be unknown. The project will use two main new ideas: 1. The recent result of the PI and Romanov. They have shown, for the first time, that the unknown potential function in the 3-dimensional Schrödinger equation can be reconstructed from the phaseless scattering data via the inversion of the Radon transform. Thus, they have addressed a long standing problem, which was posed by French mathematicians Chadan and Sabatier in 1977. This problem was about the reconstruction of the potential in the 3-dimensional Schrödinger equation from the phaseless scattering data. This step will provide good images of shapes of unknown abnormalities. However, values of abnormalities/background contrasts in refractive indices will need to be refined. This will be done using the second idea. 2. The modified globally convergent method for Inverse Scattering problem of Beilina and the PI will be used to refine values of abnormalities/background contrasts in refractive indices. More precisely, that method will be extended from its current time domain version to the frequency domain version. The approximation of the phase in the data will be taken from the first step. Global convergence theorems will be proven. Resulting numerical methods will be tested on both computationally simulated and experimental data. Experimental data will be collected by the hardware equipment which is available in the campus of University of North Carolina at Charlotte. The PI and his long term collaborator Michael A. Fiddy, Professor of Optoelectronics Center of University of North Carolina at Charlotte, are in charge of this equipment.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512330
Entities
People
- Michael Klibanov
Organizations
- Office of Naval Research
- United States Navy
- University of North Carolina