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 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 1 -regularization term. The functional is minimized with an iterative soft shrinkage-type algorithm.

A fast time-difference inverse solver for 3D EIT with application to lung imaging

“…This parameter was heuristically selected to produce the image best fitting the simulated model over 100 iterates. The sparsity algorithm specified for EIT in [22,23,38], referred to as "standard sparsity algorithm" here, the basic GPSR and BB GPSR was implemented and was continued until the threshold tol = 1e − 2. Heuristically, among a wide range of regularization parameters, = 1e − 4 produced the optimal image for both the basic and BB GPSR.…”

“…In comparison with the BB GPSR in [21], a more sophisticated version of the BB rule was employed in our study. This BB rule was similarly applied to the standard sparsity algorithm presented in "Appendix", according to [22,23,38]. The step length computed by Eq.…”

“…In this work, the PCG is implemented with the aid of the EIDORS software [19] and is regarded as the first benchmark for evaluating the performance of the proposed inverse solver. The second benchmark is the most well-known sparsity algorithm in EIT [22,23,38], which is outlined in "Appendix". For further theoretical details, the reader is referred to [22,23,38].…”

“…To best of our knowledge, the most wellknown algorithm for sparsity reconstruction in EIT was proposed in [38] and was then applied to real experiments [22,23]. Although similar to the GPSR, this algorithm follows a gradient-based method which requires solely matrix-vector products, it does not benefit from the splitting scheme in the GPSR.…”

“…Although similar to the GPSR, this algorithm follows a gradient-based method which requires solely matrix-vector products, it does not benefit from the splitting scheme in the GPSR. In addition, a direct application of the gradient of the residual leads to numerical instability for this algorithm, even in two-dimensional cases, so a Sobolev smoothing step is applied to the gradient via solving an augmented Dirichlet boundary value problem at each iterate, which increases the computational cost [22,23,38].…”