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Magnetic Resonance Electrical Impedance Tomography (MREIT) serves the purpose of imaging electrical conductivities of tissues. It is known that conductivities of most biological tissues are anisotropic. Therefore, anisotropic conductivity should not be neglected in MREIT. In this study, performance of three previously proposed anisotropic conductivity reconstruction algorithms are compared under the same conditions. Their reconstruction accuracy, spatial resolution, linearity properties and computational requirements are investigated.