Electrical Conductivity Imaging Using a Hybrid Regularization Method in Magnetic Resonance Electrical Impedance Tomography

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging technique. The harmonic-B_z algorithm in MREIT is to visualize the conductivity distribution of an electrical object Omega by using one component B_z of the magnetic flux density B = (B_x,B_y,B_z). In this paper, we present a hybrid regularization method to reconstruct the conductivity distribution in Omega from the measured B_z data contaminated with random noise. To develop this method, we propose a new stable scheme to compute nabla²B_z from the noise B_z data, and utilize the truncated singular value decomposition regularization method to solve the linear system which is ill-conditioned near the boundary of Omega. Finally, numerical examples with added white Gaussian random noise are given to show the validity of the hybrid regularization method. Our work provides a feasible way for the realization of harmonic-B_z algorithm from the noise B_z data.