SIGNAL PROCESSING BASED METHOD FOR MODELING AND SOLVING INVERSE SCATTERING PROBLEMS

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Ritter, R. (2011). SIGNAL PROCESSING BASED METHOD FOR MODELING AND SOLVING INVERSE SCATTERING PROBLEMS. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

A mature and difficult problem, still preoccupying many research communities in different application areas, is the recovery of a quantitative image of some unknown penetrable strongly scattering object. In most fields, such as ground penetrating radar, seismic and medical applications, the problem is compounded by the availability of only limited angle and noisy data. One of the more common approximate solution methods is based on diffraction tomography that relies on the first Born approximation method, which limits applications to weakly scattering situations. More sophisticated methods are typically iterative in nature, computationally intense and may not converge. We have studied an alternative nonlinear filtering approach and developed a new way to implement it, as well as evaluating different filter functions to find an optimal form. We have applied this approach to a number of classes of objects and developed a user-friendly scattered field simulator as a resource for this and related inverse scattering problems. We also re-investigated the widely accepted limitations of the first Born approximation and found that when close to a scattering resonance, the first Born approximation can yield a good estimate of the object's scattering cross section. Tied to all of these imaging applications is the issue of limited data: how many sources and how many receivers are required for a given quality and reliability of the resulting image. We took a fundamental look at this issue in terms of the number of degrees of freedom of the entire source-measurement domain and deduced clear guidelines on the minimum data sets necessary that should be measured, in order to expect a reasonable image.

Details
Author

Ritter, Richard

Title

SIGNAL PROCESSING BASED METHOD FOR MODELING AND SOLVING INVERSE SCATTERING PROBLEMS

Physical Description

1 online resource (226 pages) : PDF

Date

2011

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

A mature and difficult problem, still preoccupying many research communities in different application areas, is the recovery of a quantitative image of some unknown penetrable strongly scattering object. In most fields, such as ground penetrating radar, seismic and medical applications, the problem is compounded by the availability of only limited angle and noisy data. One of the more common approximate solution methods is based on diffraction tomography that relies on the first Born approximation method, which limits applications to weakly scattering situations. More sophisticated methods are typically iterative in nature, computationally intense and may not converge. We have studied an alternative nonlinear filtering approach and developed a new way to implement it, as well as evaluating different filter functions to find an optimal form. We have applied this approach to a number of classes of objects and developed a user-friendly scattered field simulator as a resource for this and related inverse scattering problems. We also re-investigated the widely accepted limitations of the first Born approximation and found that when close to a scattering resonance, the first Born approximation can yield a good estimate of the object's scattering cross section. Tied to all of these imaging applications is the issue of limited data: how many sources and how many receivers are required for a given quality and reliability of the resulting image. We took a fundamental look at this issue in terms of the number of degrees of freedom of the entire source-measurement domain and deduced clear guidelines on the minimum data sets necessary that should be measured, in order to expect a reasonable image.

Genre

doctoral dissertations

Subjects--Topics

Electrical engineering
Optics
Engineering

Degree

Ph.D.

Keywords

Born Approximation
Cepstral
Degrees of Freedom
Homomorphic Filtering
Inverse Scattering
Lorenz Mie

Subject Area

Electrical Engineering

Advisor(s)

Fiddy, Michael

Committee Members

Casperson, Lee
Hasan, Mohamed-Ali
Ras, Zbigniew

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2011.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Ritter_uncc_0694D_10247

Permalink

http://hdl.handle.net/20.500.13093/etd:901