Electrical impedance tomography (EIT) is an imaging modality with many possible practical applications. It is mainly used for geophysical applications, for which it is called electrical resistivity tomography. There have also been many proposed medical applications such as respiratory monitoring and breast tumour screening. Although there have been many uniqueness and stability results published over the last few decades, most of the results are in the context of the theoretical continuous problem. In practice however, we almost always have to solve a discretised problem for which very few theoretical results exist. In this thesis we aim to bridge the gap between the continuous and discrete problems. The first problem we solve is the three-dimensional triangulation problem of uniquely embedding a tetrahedral mesh in R3. We parameterise the problem in terms of dihedral angles and we provide a constructive procedure for identifying the independent angles and the independent set of constraints that the dependent angles must satisfy. We then use the implicit function theorem to prove that the embedding is locally unique. We also present a numerical example to illustrate that the result works in practice. Without the understanding of the geometric constraints involved in embedding a three-dimensional triangulation, we cannot solve more complex problems involving embeddings of finite element meshes. We next investigate the discrete EIT problem for anisotropic conductivity. It is well known that the entries of the finite element system matrix for piecewise linear potential and piecewise constant conductivity are equivalent to conductance values of resistors defined on the edges of the finite element mesh. We attempt to tackle the problem of embedding a finite element mesh in R3, such that it is consistent with some known edge conductance values. It is a well known result that for the anisotropic conductivity problem, the boundary data is invariant under diffeomorphisms that fix the boundary. Before investigating this effect on the discrete case, we define the linear map from conductivities to edge conductances and investigate the injectivity of this map for a simplistic example. This provides an illustrative example of how a poor choice of finite element mesh can result in a non-unique solution to the discrete inverse problem of EIT. We then extend the investigation to finding interior vertex positions and conductivity distributions that are consistent with the known edge conductances. The results show that if the total number of interior vertex coordinates and anisotropic conductivity variables is larger than the number of edges in the mesh, then there exist discrete diffeomorphisms that perturb the vertices and conductivities such that no change in the edge conductances is observed. We also show that the non-uniqueness caused by the non-injectivity of the linear map has a larger effect than the non-uniqueness caused by diffeomorphism invariance.

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. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

No description available.

No description available.

Not available / text

Predicting tenderness in today's beef supply could be advantageous to packers and consumers. In this study (n = 1,137 carcasses), visible-near-infrared, electrical impedance, pH and Minolta CIE L*, a*, and b* color space values were examined as predictors of beef 1, 7, and 14 d Warner-Bratzler (N) or Slice Shear (N) force values as estimators of beef tenderness. Visible-NIR at 350 to 1830 nm, electrical impedance, and color space values were taken at the beef packing plant, along with carcass data. Strip loins were transported to Texas A & M University where pH was taken. Six steaks were taken from the anterior end of the strip loin and randomly assigned to either Warner-Bratzler shear force (WBSF) after 1, 7, or 14 days, or Slice shear force (SSF) after 1, 7, and 14 days of post-harvest aging at 2 degrees C. Shears were taken on assigned days. Shear force values were highly correlated with each other (r = 0.37 to 0.56 for WBSF and r = 0.75 to 0.78 for SSF) (P < 0.05). Within the independent variables, reflectance values for mid-range wavelengths (562nm-1193nm) were found to be most highly correlated with the dependent variables (P < 0.05). pH and color spaces values were more highly correlated (P < 0.05) to slice shears values then to Warner-Bratzler shears force values. Electrical impedance was the least significant with r values of 0.00 to 0.14. When Visble-NIR reflectance values were used in stepwise regression equations to predict 1, 7, or 14 d WBSF or 1, 7, or 14 d SSF, prediction equations for 14 d WBSF and SSF had the highest R^2 (0.14 and 0.36, respectively). Stepwise regression equations that included pH and color space values had the highest R^2 for 7 d WBSF and 1 d SSF (0.22 and 0.28, respectively). Electrical impedance alone in a stepwise regression equation had the highest R^2 for 1 and 14 d WBSF and 1 and 7 d SSF (0.02 and 0.03, respectively). Stepwise regression equations that included pH, color space values, and electrical impedance had the highest R^2 for 7 d WBSF and 14 d SSF (0.25 and 0.24, respectively). When pH, color space values, electrical impedance, and Visible-NIR were used, 7 d WBSF and 1 d SSF had the highest R^2 (0.38 and 0.34, respectively). Stepwise regression equations that included pH, color space values, and Visible-NIR had the highest R^2 for 7 d WBSF and 14 d SSF (0.30 and 0.44, respectively). For predicting 14 d Warner-Bratzler shear force, a R^2 of 0.20 was found using Visible-NIR, pH and color space values. When used, the partial least squares equation predicted tenderness with an 85 percent success rate. For predicting 14 d Slice shear forces, a R^2 of 0.40 was found. When used, the partial least squares equation had a 100 percent success rate of predicting those steaks found tender to be tender for Slice shear force. There was an 85 percent success rate for predicting 14 d Warner-Bratzler shear forces. Both equations still had little to no success in predicting tough steaks. The Visible-NIR can successfully predict tenderness

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [113]-116).

Thesis (Ph. D.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2007. / Includes bibliographical references (p. 161-167).

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains ix, 131 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 121-131).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Roger T. Bonnecaze. Vita. Includes bibliographical references.