Global maxwell tomography: A novel technique for electrical properties mapping based on MR measurements and volume integral equation formulations

A new, MR-based algorithm for the estimation of electrical properties (permittivity and conductivity) is presented. The algorithm is based on a volume integral equation formulation that represents scatterers in terms of equivalent currents. Set up as an unconstrained optimization problem, the algorithm iterates over estimates of electrical properties to minimize the error between measured and simulated flux densities. For the two presented numerical examples, the algorithm effectively reconstructs the true distribution of electrical properties when starting from corrupted initial guesses.