Non-iterative conductivity reconstruction algorithm using projected current density in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the current density and the conductivity distribution in an electrical object Omega using the measured magnetic flux data by an MRI scanner. MREIT uses only one component B(z) of the magnetic flux density B = (B(x), B(y), B(z)) generated by an injected electrical current into the object. In this paper, we propose a fast and direct non-iterative algorithm to reconstruct the internal conductivity distribution in Omega with the measured B(z) data. To develop the algorithm, we investigate the relation between the projected current density J(P), a uniquely determined component of J by the map from current J to measured B(z) data and the isotropic conductivity. Three-dimensional numerical simulations and phantom experiments are studied to show the feasibility of the proposed method by comparing with those using the conventional iterative harmonic B(z) algorithm.