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 Calderón'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 Calderón'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 Calderón's special functions in the interior. Furthermore, in three dimensions and higher, Calderón'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.