Sparse 3D reconstructions in electrical impedance tomography using real data. (English) Zbl 1304.65242
Summary: 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.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 92C55 | Biomedical imaging and signal processing |
Keywords:
electrical impedance tomography; sparsity reconstruction; Tikhonov regularization; experimental dataReferences:
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