Inverse conductivity problem for inaccurate measurements

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Abstract
In order to determine the conductivity of a body or of a region of the Earth using electrical prospecting, currents are injected on the surface, surface voltage responses are measured, and the data are inverted to a conductivity distribution. In the present paper a new approach to the inverse problem is considered for measurements containing noise in which data are optimally chosen using available a priori information at the time of the imaging. For inexact data the eigenvalues of the current-to-voltage boundary mapping show what part of the conductivity function can be confidently restored from the measurements. A special choice of measurements permits simple inversion algorithms reconstructing only this reliable part of the solution, hence reducing the dimension of the inverse problem. The inversion approach is illustrated in application to numerical modelling via a very fast approximate imaging solution.