Electrical impedance tomography is an imaging method with applications to geophysics and medical imaging. A new approximation is presented based on Nachman's 2-dimensional construction for closed domains. It improves upon existing approximations by extending the range of application from resolving 2 times the surface conductivity to imaging perfect conductors and insulators. With perfect knowledge of boundary data, this approximation exactly resolves a single conductive disc embedded in a homogenous domain. The problem, however, is ill-posed, and imaging performance degrades quickly as the distance from the boundary increases. The key to the approximation lies in (a) approximating Fadeev's Green's function (b) pre-processing measured voltages based on a boundary-integral equation (c) solving a linearized inverse problem (d) solving a d-bar equation, and (e) scaling the resulting image based on analytical results for a disc. In the development of the approximation, a new formula for Fadeev's Green's function is presented in terms of the Exponential Integral function. Also, new comparisons are made between reconstructions with and without solving the d-bar equation, showing that the added computational expense of solving the d-bar equation is not justified for radial problems. There is no discernible improvement in image quality. As a result, the approximation converts the inverse conductivity problem into a novel one-step linear problem with pre-conditioning of boundary data and scaling of the resulting image. Several extensions to this work are possible. The approximation is implemented for a circular domain with unit conductivity near the boundary, and extensions to other domains, bounded and unbounded should be possible, with non-constant conductivity near the boundary requiring further approximation. Ultimately, further research is required to ascertain whether it is possible to extend these techniques to imaging problems in three dimensions.

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The ARG (Acoustic Research Group) at the University of Canterbury has a goal to image objects buried under the seafloor. In order to image these objects, accurate models and a good understanding of the acoustic parameters of the seafloor are needed. The relevant acoustic parameters to model the seafloor include: physical classification, speed of sound, acoustic impedance, density, and roughness. Acquiring accurate acoustic parameters for the seafloor is a challenging task that requires different approaches depending on the environment, especially in locations with low visibility. This thesis looks at a non-invasive method of acoustically examining the roughness spectrum and acoustic impedance of the seafloor. To achieve these goals, spherical transducers with a continuous bandwidth between 30 kHz and 130 kHz were chosen to examine the frequency dependent specular and diffused components of the reflection from rough seafloor surfaces. Using spherical transducers allows the surface scattering to be examined independently of the transducer beam-pattern. This thesis examines the range and validity of the tools required to make these measurements and presents empirical results measured in the controlled environment of a cylindrical 3.5m diameter by 2m deep sonar test tank. Using results from the sonar test tank, this thesis demonstrates that the acoustic impedance, speed of sound, and density of the material of the seafloor can be measured from a single seafloor realisation measured at multiple angles, provided the seafloor material has a critical angle. Additionally, this thesis demonstrates that the spectrum of the specular and diffused components of the rough-surface reflection requires averaging multiple seafloor realisations to be statistically relevant. As well as describing the benefits of using spherical transducers, this thesis presents some of the problems and potential solutions for future applications.

Thesis (Ph. D.)--University of Hawaii at Manoa, 1996. / Includes bibliographical references (leaves 227-230). / Microfiche. / xxii, 230 leaves, bound ill. 29 cm

Electrical impedance tomography is an imaging method with applications to geophysics and medical imaging. A new approximation is presented based on Nachman's 2-dimensional construction for closed domains. It improves upon existing approximations by extending the range of application from resolving 2 times the surface conductivity to imaging perfect conductors and insulators. With perfect knowledge of boundary data, this approximation exactly resolves a single conductive disc embedded in a homogenous domain. The problem, however, is ill-posed, and imaging performance degrades quickly as the distance from the boundary increases. The key to the approximation lies in (a) approximating Fadeev's Green's function (b) pre-processing measured voltages based on a boundary-integral equation (c) solving a linearized inverse problem (d) solving a d-bar equation, and (e) scaling the resulting image based on analytical results for a disc. In the development of the approximation, a new formula for Fadeev's Green's function is presented in terms of the Exponential Integral function. Also, new comparisons are made between reconstructions with and without solving the d-bar equation, showing that the added computational expense of solving the d-bar equation is not justified for radial problems. There is no discernible improvement in image quality. As a result, the approximation converts the inverse conductivity problem into a novel one-step linear problem with pre-conditioning of boundary data and scaling of the resulting image. Several extensions to this work are possible. The approximation is implemented for a circular domain with unit conductivity near the boundary, and extensions to other domains, bounded and unbounded should be possible, with non-constant conductivity near the boundary requiring further approximation. Ultimately, further research is required to ascertain whether it is possible to extend these techniques to imaging problems in three dimensions.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Robert Butera; Committee Member: Pamela Bhatti; Committee Member: Todd McDevitt

Thesis (Ph. D.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains vii, 118 p. : ill. Includes abstract. Includes bibliographical references.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 93). Also available in electronic version. Access restricted to campus users.

Thesis (M.S.)--University of Wisconsin--Madison, 1942. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.