An Implementation of CalderÓn´s Method for 3-D Limited-View EIT

Mathematical interest in electrical impedance tomography has been strong since the publication of Calderon´s foundational paper. This paper introduced the idea of applying external voltage patterns to a medium such that, assuming that the medium is sufficiently close to a constant admittivity, the reconstruction can be accomplished directly by inverse Fourier transform. Motivated by Calderon´s method, we have developed a variant of the algorithm which is applicable to the case of measurement on only a part of the boundary and on discrete electrodes. Here we determine voltage or current patterns to apply to the electrodes which optimally approximate Calderon´s special functions in the interior. Furthermore, in three dimensions and higher, Calderon´s method allows each point in Fourier space to be computed in a multiplicity of ways. We show that by making use of the inherent redundancy in our measurements, we can significantly improve the quality of the static images produced by our algorithm.