A Novel two-step approach for magnetic resonance electrical properties tomography

In this paper, a novel inversion approach to retrieve the electromagnetic properties of human tissues from magnetic resonance imaging data is presented. To face the non-linearity and ill-posedness of the inverse problem, the proposed approach splits the inversion task into two steps. In the first step, the contrast source and the electric field within the region of interest are estimated from the magnetic resonance data. In the second step, the constitutive relationship between the contrast sources and fields distributions is exploited to reconstruct the electromagnetic properties. Notably, the separation in two steps of the solution of the inverse problem allows tackling it as a cascade of linear steps, with a remarkable impact on the problem solution and computational burden. Moreover, in the second step a priori information-such as tissue segmentation-can be easily incorporated for a flexible and reliable reconstruction of the tissue properties. The proposed approach is validated with full 3D realistic simulations, showing that its results positively compare with other integral equation-based state of the art approaches.