Electrical Impedance Tomography gives rise to the severely ill-posed Calder?ón problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing equation. The electrical conductivity of an object is of interest in many fields, notably medical imaging, where applications may vary from stroke detection to early detection of breast cancer.
The uniqueness and stability questions for the three-dimensional problem were largely answered in the affirmative in the 1980's using complex geometrical optics solutions, and this led further to a direct reconstruction method relying on a non-physical scattering transform.
In this talk we look at a direct reconstruction algorithm for the three-dimensional Calderón problem in the scope of regularization. Indeed, a suitable and explicit truncation of the scattering transform gives a stable and direct reconstruction method that is robust to small perturbations of the data. Numerical tests on simulated noisy data illustrate the feasibility and regularizing effect of the method, and suggest that the numerical implementation performs better than predicted by theory.