Magnetic resonance-based imaging of human electric properties with phaseless contrast source inversion

Magnetic resonance imaging scanners can provide, by B1-mapping techniques, measurements of the transmit sensitivity magnitude, whereas the transmit sensitivity phase can only be approximated under symmetry assumptions of the coil and the sample. Nonetheless, up to now many techniques have been proposed to retrieve electric properties maps at radiofrequency by elaborating the complex transmit sensitivity. These techniques are usually referred to as magnetic resonance-based electric properties tomography. In order to perform imaging of the elecric properties also in cases which do not fulfill the assumptions for transmit sensitivity phase estimation, a variation of the phaseless contrast source inversion technique is proposed in this paper to retrieve the electric properties by elaborating only the magnitude of the transmit sensitivity. The novel technique is described in a generalised framework based on a functional viewpoint and it is specialised to deal with two-dimensional boundary-free problems. Moreover, a phaseless back propagation solution is proposed as initial guess. The proposed technique and initial guess have been tested on realistic two-dimensional model problems, which show that the numerical minimisation converges towards the global minimum when multiple linearly independent measurements are provided and that it is quite robust with respect to noisy inputs.