Reconstruction of biologic tissue conductivity from noisy magnetic field by integral equation method

Magnetic resonance electrical impedance tomography (MREIT) is a new technique to recover the conductivity of biologic tissue from the induced magnetic flux density. This paper proposes an inversion scheme for recovering the conductivity from one component of the magnetic field based on the nonlinear integral equation method. To apply magnetic fields corresponding to two incoherent injected currents, an alternative iteration scheme is proposed to update the conductivity. For each magnetic field, the regularizing technique on the finite dimensional space is applied to solve an ill-posed linear system. Compared with the well-developed harmonic Bz method, the advantage of this inversion scheme is its stability, since no differential operation is required on the noisy magnetic field. Numerical implementations are given to show the convergence of the iteration and its validity for noisy input data.