This is the first of three papers summarizing the use of electrical impedance excitation/measurement for producing cross-sectional images of the distribution of insulating media imbedded in conducting media. This computed tomographic approach finds the distribution of electrical properties of an electric field which minimizes in the least squares sense the difference between measured and computed boundary response to excitation. In this paper we first describe the basic analytical methods developed for imaging a two-dimensional field. These methods include a description of our block decomposition method for coarse mesh computations which are then decomposed to provide fine mesh details with three orders-of-magnitude savings in computational effort. We then extend these methods to quasi three-dimensional imaging, add a method for preconditioning voltages for error correction, describe methods for optimizing the resolution of a target by providing optimal excitation patterns and then describe the overall numerical sensitivity of the system.
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