Mathematical Algorithms for Multidimensional Inverse Scattering Problems in Inhomogeneous Medium.
Abstract
Multidimensional inverse scattering problems (ISP) in inhomogeneous media have important and extensive applications in many areas of interest to the NAVY. Among them are ocean acoustics, electromagnetic properties of sea ice, oceanic biology, and non-invasive testing of some materials, including semiconductors. From mathematical point of view the numerical methods must be based on robust and efficient mathematical algorithms. The development of such algorithms with rapid convergence rates is a challenging task in the theory of multidimensional ISP. In fact, ISPs represent an alternative to the conventional X-ray tomography. The major difficulty of the ISPs is that waves propagate in different (unknown) directions rather than just along straight lines, as it is in the case with X-ray tomography. Thus another term for ISPs is diffusion tomography . We have been working on theoretical studies and computational testing of numerical methods for Inverse Scattering Problems (ISP). Our main efforts have been concentrated on 3-Dimensional ISP. A more minor effort was devoted to 1-D phaseless ISP, that is ISP without phase information.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADA266440
Entities
People
- Michael Klibanov
Organizations
- University of North Carolina at Charlotte