Total Variation regularisation in EIT Reconstruction

Andrea Borsic1, Christopher N. McLeod1, William R.B. Lionheart2

1 School of Engineering, Oxford Brookes University, aborsic@brookes.ac.uk

2 Department of Mathematics, UMIST

ABSTRACT

Electrical Impedance Tomography is an ill-posed inverse problem. Regularisation techniques are adopted in order to stabilise the reconstruction. The problem is formulated as the minimisation of the sum of two terms: the first is the mismatch between the real measurements and simulated ones, the second is the regularisation functional. The functional accomplishes the task of stabilising the inversion by assuming large values corresponding to conductivity distributions that are unlikely. Such images are therefore rejected by the minimisation process. The choice of a regularisation functional selects the class in which the inverse solutions will lie.

Commonly adopted regularisation functionals in EIT penalise non-smooth images, rendering the reconstruction algorithm incapable of describing step conductivity distributions. Situations where the imaged body has a non continuous conductivity distribution are of practical interest both in process and medical imaging. Total Variation regularisation is an emerging technique that we believe is particularly successful for solving such problems. The technique involves a regularisation functional which is not differentiable everywhere. An appropriate framework for solving the problem efficiently is presented in this paper.

Keywords Electrical Impedance Tomography, Total Variation, Primal Dual Interior Point Methods