We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, 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 ℓ1-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ℓ1-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. © 2011 Elsevier B.V. All rights reserved.
Gehre, M., Kluth, T., Lipponen, A., Jin, B., Seppnen, A., Kaipio, J. P., & Maass, P. (2012). Sparsity reconstruction in electrical impedance tomography: An experimental evaluation. In Journal of Computational and Applied Mathematics (Vol. 236, pp. 2126–2136). https://doi.org/10.1016/j.cam.2011.09.035