Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality providing high resolution conductivity images based on the current injection MRI technique. In contrast to electrical impedance tomography (EIT), the MREIT system utilizes the internal information of current density distribution which plays an important role in eliminating the ill-posedness of the inverse problem in EIT. It has been shown that the J-substitution algorithm in MREIT reconstructs conductivity images with higher spatial resolution. However, fundamental mathematical questions, including the uniqueness of the MREIT problem itself and the convergence of the algorithm, have not yet been answered. This paper provides a rigorous proof of the uniqueness of the MREIT problem and analyses the convergence behaviour of the J-substitution algorithm.

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