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 discontinuities 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 interphase 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 which cannot 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. This paper introduces the smoothing properties of the traditional quadratic regularization algorithms, the discontinuity preserving properties of the TV functional are then outlined. The paper follows introducing the general PD-IPM framework and its application to inverse problems. Specifically 2D and 3D results from the application of TV regularization to the EIT inverse problem are presented and analyzed. Trough practical examples the discontinuity preserving capabilities of A. Borsic is with the Thayer School of Engineering, Dartmouth College, USA, email: [email protected] B. M. Graham is with the School of Information Technology and Engineering (SITE), University of Ottawa, Canada, email: [email protected] A. Adler is with the Department of Systems and Computer Engineering, Cartleton University, Canada, email: [email protected] W. R. B. Lionheart is with the School of Mathematics, University of Manchester, Manchester, UK, email: [email protected]