Total variation regularization with reduced basis in electrical impedance tomography
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It is demonstrated that resorting to reduced bases can speed up a reconstruction algorithm based on combining the lagged diffusivity algorithm with sequential linearizations and preconditioned LSQR iteration without any significant loss of reconstruction quality or of the edge-enhancing nature of total variation regularization. The ideas are numerically tested in three dimensions on unstructured finite element meshes with both simulated and experimental data, resulting in online reconstruction times of only a few seconds on a standard laptop computer.