Magnet Resonance Electrical Impedance Tomography (MREIT): Convergence and Reduced Basis Approach
For researchers in MREIT, this work provides a faster reconstruction algorithm with theoretical guarantees, though the improvement is incremental.
The paper extends the convergence theory of the Harmonic B_z algorithm for MREIT, showing that an approximate forward PDE solution suffices for convergence. It then develops a novel algorithm combining this with an adaptive reduced basis method, achieving faster reconstruction of a high-resolution Shepp-Logan phantom.
This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a solution algorithm are presented. The convergence theory of this algorithm is extended, such that the usage an approximative forward solution of the underlying partial differential equation (PDE) in the algorithm is sufficient for convergence. Motivated by this result, a novel algorithm is developed where it is the aim to speed-up the existing Harmonic $B_z$ Algorithm. This is achieved by combining it with an adaptive variant of the reduced basis method, a model order reduction technique. In a numerical experiment a high-resolution image of the shepp-logan phantom is reconstructed and both algorithms are compared.