Sparse 3D reconstructions in electrical impedance tomography using real data

Abstract

We present a 3D reconstruction algorithm with sparsity constraints for electrical impedance tomography (EIT). EIT is the inverse problem of determining the distribution of conductivity in the interior of an object from simultaneous measurements of currents and voltages on its boundary. The feasibility of the sparsity reconstruction approach is tested with real data obtained from a new planar EIT device developed at the Institut für Physik, Johannes Gutenberg Universität, Mainz, Germany. The complete electrode model is adapted for the given device to handle incomplete measurements and the inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ${\ell }^1$-regularization term. The functional is minimized with an iterative soft shrinkage-type algorithm.

Keywords:

• electrical impedance tomography
• sparsity reconstruction
• Tikhonov regularization
• breast cancer detection
• experimental data

Acknowledgments

We would like to thank Professor Karl Schilcher, Professor Hubert Spisberger and Dr Heinz Georgi from the Institut für Physik, Johannes Gutenberg Universität, Mainz, Germany, for providing us the real data collected using the latest planar EIT device designed by their research group. Without their generosity and support of any scientic progress which might lead to breakthroughs for detecting breast cancer by means of EIT, this work would not have been possible. We would also like to thank Dr Bangti Jin for his valuable comments in the preparation of the manuscript.