Theory and applications of scattering and inverse scattering problems
Wang, Yi-Ming
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Permalink
https://hdl.handle.net/2142/20988
Description
Title
Theory and applications of scattering and inverse scattering problems
Author(s)
Wang, Yi-Ming
Issue Date
1991
Doctoral Committee Chair(s)
Chew, Weng Cho
Department of Study
Electrical and Computer Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
Two algorithms based on the recursive operator algorithm are proposed to solve for the scattered field from an arbitrarily shaped, inhomogeneous scatterer. By discretizing the object into N subobjects, the scattering solution of an arbitrarily shaped inhomogeneous scatterer can be formulated as a scattering solution of an N-scatterer problem, each of whose scattered fields is approximated by M harmonics. Using the translation formulas, a recursive approach is developed which enables us to derive an n + 1-scatterer solution from an n-scatterer solution. Therefore, knowing the isolated transition matrices for all subscatterers, the total transition matrices for an N-scatterer problem can be obtained recursively. The computation time of such an algorithm is proportional to $N\sp2M\sp2P$, where P is the number of harmonics used in the translation formulas. Furthermore, by introducing an aggregate transition matrix to the recursive scheme, a fast algorithm, whose computational complexity is linear in N, is developed. The algorithm has been used to solve for the scattering solution of a 10$\lambda$ diameter, two-dimensional dielectric scatterer with about 12,000 unknowns, taking 32 sec on a CRAY-2 supercomputer.
In order to solve the electromagnetic inverse scattering problem beyond the Born approximation, two iterative algorithms are developed. They are the Born iterative method and the distorted Born iterative method. Numerical simulations are performed in several cases in which the conditions for the Born approximation are not satisfied. The results show that in both low and high frequency cases, good reconstructions of the permittivity distribution are obtained. Meanwhile, the simulations reveal that each method has its advantages. The distorted Born iterative method shows a faster convergence rate compared to that for the Born iterative method, while the Born iterative method is more robust to noise contamination compared to that for the distorted Born iterative method.
A boosting procedure which helps to retrieve the maximum amount of information content is proposed to solve the limited angle inverse scattering problem. Using the boosting procedure in the limited angle inverse scattering problem, good reconstructions are achieved for both well-to-well tomography and subsurface detection.
By applying the fast recursive algorithm to the solution of the direct scattering part of the iterative schemes and the conjugate gradient method to the solution of the inversion part of the iterative schemes, the computational complexity of the Born iterative method and the distorted Born iterative method is further reduced from $N\sp3$ to $N\sp2$.
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