On Optimal Current Patterns for Electrical Impedance

We develop a statistical criterion for optimal patterns in planar circular electrical impedance tomography. These pat- terns minimize the total variance of the estimation for the resis- tance or conductance matrix. It is shown that trigonometric pat- terns (Isaacson, 1986), originally derived from the concept of dis- tinguishability, are a special case of our optimal statistical patterns. New optimal random patterns are introduced. Recovering the elec- trical properties of the measured body is greatly simplified when optimal patterns are used. The Neumann-to-Dirichlet map and the optimal patterns are derived for a homogeneous medium with an arbitrary distribution of the electrodes on the periphery. As a spe- cial case, optimal patterns are developed for a practical EIT system with a finite number of electrodes. For a general nonhomogeneous medium, with no a priori restriction, the optimal patterns for the resistance and conductance matrix are the same. However, for a ho- mogeneous medium, the best current pattern is the worst voltage pattern and vice versa. We study the effect of the number and the width of the electrodes on the estimate of resistivity and conduc- tivity in a homogeneous medium. We confirm experimentally that the optimal patterns produce minimum conductivity variance in a homogeneous medium. Our statistical model is able to discrim- inate between a homogenous agar phantom and one with a 2 mm air hole with error probability (p-value) 1/1000.

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