On the Convergence of the Harmonic Bz Algorithm in Magnetic Resonance Electrical Impedance Tomography

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging technique that aims to provide electrical conductivity images with sufficiently high spatial resolution and accuracy. A new MREIT image reconstruction method called the harmonic $B_z$ algorithm was proposed in 2002, and it is based on the measurement of $B_z$ that is a single component of an induced magnetic flux density $\mathbf{B}=(B_x,B_y,B_z)$ subject to an injection current. Since then, MREIT imaging techniques have made significant progress, and recent published numerical simulations and phantom experiments show that we can produce high-quality conductivity images when the conductivity contrast is not very high. Though numerical simulations can explain why we could successfully distinguish different tissues with small conductivity differences, a rigorous mathematical analysis is required to better understand the underlying physical and mathematical principle. The purpose of this paper is to provide such a mathematica...

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