Abstract of the paper ``Weighted least-squares methods for electrical impedance tomography'' with Jeffrey S. Kallman

Methods are developed for design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity, an algorithm with the following properties is found:

(1) The optimum constant for the starting model is determined automatically.

(2) The weighted least-squares error between the predicted and measured power dissipation data is as small as possible.

(3) The variance of the reconstructed conductivity from the starting model is minimized.

(4) Potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized.

(5) Cells with most coverage tend to deviate least from the background value.

The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background conductivity remains invariant, while the optimum contributions in orthogonal directions are found. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties.

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