A Total Variance Regularization Method for Conductivity Imaging Using MR Phase

This paper proposed a total variation regularization method for conductivity imaging using MR phase only. This method does not use the assumption that conductivity distribution is locally constant which is usually done. It improves the accuracy of conductivity imaging and more robust against the noise. Starting from the Maxell's equations, we can get a partial differential equation (PDE) including the gradients of conductivity. Through using finite difference method, the equation was transformed into linear system form. Different from the previous method, it was solved by minimizing residues squares regularized by a total variation term. It does not need to give the boundary values of region of interest (ROI) of an object and add a diffusion term. The total variation term reduces the effect of noise and spurious oscillations in this method. The proposed method was compared with the conventional method which is using locally constant assumption. This method has been conducted in simulation and human experiment. Simulation experiment results of the proposed method shows lower reconstruction errors and more robust to the noise compared to conventional method. In human brain experiment, the result of proposed method shows more structures than conventional method. The total variation regularization method for conductivity imaging improve the accuracy of conductivity maps and reduce noise, it has the potential for clinical applications.