| Electrical impedance tomography is a rapidly growing discipline with an increasing number of medical and nonmedical applications. Many recent studies indicate that while the technique shows promise, improvements must be made before impedance imaging systems take their place beside more mature imaging technologies in the clinic and in the laboratory. This dissertation is an effort to address two of the shortcomings of currently available impedance tomography systems. First, a new numerical solution to the governing partial differential equation is presented which allows the user a fast, easy means of making geometrical changes. Treating the domain of interest as an input to the problem, recent results from the field of wavelet theory provide a simple means of identifying the boundary as well as giving a method for solving the partial differential equation in a fast, efficient manner. Since the algorithm only requires a pixel representation of the geometry and does not use a grid generation program, it may be of interest in applications where the geometry varies with time or the user may not be familiar with the complexities of typical finite element method grid generation programs. Second, an application of the conjugate gradient method to the problem of regularizing the nonlinear Newton-Raphson conductivity update leads to significant improvement over the popular Levenberg-Marquardt trust region regularization. The use of the conjugate gradient method as a regularization technique allows for convergence of the conductivity reconstruction in far fewer iterations and can perform reconstructions with an initial assumption of uniform conductivity in situations where other methods require either a priori knowledge or internal measurement of voltages. |
