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Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx,By,Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.