Total Variation Regularization in Electrical Impedance Tomography

This paper presents an evaluation of the use of Primal Dual Methods for efficiently regularizing the electric impedance tomography (EIT) problem with the Total Variation (TV) functional. The Total Variation functional is assuming an important role in the regularization of inverse problems thanks to its ability to preserve dis- continuities in reconstructed profiles. This property is desirable in many fields of application of EIT imaging, such as the medical and the industrial, where inter-organ boundaries, in the first case, and inter-phase boundaries, in the latter case, present step changes in electrical properties which are difficult to be reconstructed with traditional regularization methods, as they tend to smooth the reconstructed image. Though desirable, the TV functional leads to the formulation of the inverse problem as a minimization of a non-differentiable function whichcannot be efficiently solved with traditional optimization techniques such as the Newton Method. In this paper we demonstrate the use of Primal Dual - Interior Point Methods (PD-IPM) as a framework for TV regularized inversion