Abstract
We propose a novel, variational inversion methodology for the electrical impedancetomography (EIT) problem, where we seek electrical conductivity σinside a bounded, simply connected domain Ω,given simultaneous measurements of electric currentsI and correspondingpotentials Vat the boundary. Explicitly, we make use of natural, variationalconstraints on the space of admissible functions σ, toobtain efficient reconstruction methods which make best use of the data.We give a detailed analysis of the variational constraints; we propose avariety of reconstruction algorithms for the static problem in a simplecontinuum model. We discuss their advantages and disadvantages and we assessthe performance of our algorithms through numerical simulations andcomparisons with other, well established, numerical reconstruction methods.
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