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.

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Maxwell's equations are transformed from a Cartesian geometry to a Riemannian geometry. A geodetic path in the Riemannian geometry is defined as the raypath on which the electromagnetic energy efficiently travels through the medium. Consistent with the spatial behavior of the Poynting vector, the metric tensor is required to be functionally dependent on the refractive index of the medium. A symmetric nonorthogonal transformation is introduced, in which the metric is a function of an electromagnetic tension. This so-called refractional tension determines the curvature of the geodetic line. To verify the geodetic propagation paths and wavefronts, a spherical object with a refractive index not equal to one is considered. A full 3-D numerical simulation based on a contrast-source integral equation for the electric field vector is used. These experiments corroborate that the geodesics support the actual wavefronts. This result has consequences for the explanation of the light bending around the Sun. Next to Einstein's gravitational tension there is room for an additional refractional tension. In fact, the total potential interaction energy controls the bending of the light. It is shown that this extended model is in excellent agreement with historical electromagnetic deflection measurements.@en