Improved Multiplicative Regularization for CSI-EPT

We present an improved multiplicative Contrast Source Inversion (CSI) approach for Electrical Properties Tomography (EPT). In EPT, the conductivity and permittivity profiles of a body part are reconstructed based on a known circularly polarized part of the magnetic field (the $B_{1}^+$ -field) that has its support inside the body part of interest. The CSI method attempts to reconstruct these profiles in an iterative and alternating manner by first fixing the contrast and updating the contrast source (product of tissue contrast and electric field) and subsequently fixing the contrast source and updating the contrast. In this paper, regularization is included in a multiplicative way similar to the standard multiplicative CSI-EPT method. However, the regularized objective function is different and an update for the contrast is obtained through one-step Jacobi filtering of a least-squares reconstruction that is based on the updated contrast source. Two-dimensional numerical experiments for conductivity and permittivity tissue profiles of a female body model show that, for data with various noise levels, the proposed regularization approach generally provides improved tissue reconstructions compared with standard multiplicative CSI-EPT.