Total variation regularization with reduced basis in electrical impedance tomography

TL;DR

This paper introduces a reduced basis approach to accelerate total variation regularization in electrical impedance tomography, achieving rapid 3D reconstructions with minimal quality loss on standard hardware.

Contribution

It demonstrates that reduced basis techniques can significantly speed up TV regularization in EIT without compromising reconstruction quality or edge preservation.

Findings

Reconstruction times reduced to a few seconds on a laptop.

No significant loss in image quality or edge features.

Applicable to 3D unstructured finite element meshes with real data.

Abstract

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.