We derive an explicit formula to compute the negative circularly polarized component of the magnetic field, $$$H^-$$$, from the measured positively polarized component, $$$H^+$$$, for magnetic resonance electrical properties tomography (MREPT). Then, using the measured $$$H^+$$$ and the computed $$$H^-$$$, a novel regularization term for MREPT is introduced based on the $$$x$$$- and $$$y$$$-components of Ampere’s law and the $$$z$$$-component of Faraday’s law that have not been used so far for the reconstruction of EPs. This physically reasonable constraint well regularizes EPs at low convection field region.
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