On the conductivity imaging by MREIT: Available resolution and noisy effect

Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT), MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. This paper aims to give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm, one of the well-implementation MREIT algorithms. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.