Sparsity reconstruction in electrical impedance tomography: an experimental evaluation
The paper investigates the potential of sparsity constraints in the electrical impedance tomography inverse problem. In this setting, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This information is incorporated into the regularized term of a Tikhonov-type functional. The algorithm is based on the interactive soft shrinkage method introduced by \textit{I. Daubechies, M. Defrise} and \textit{C. De Mol} [Commun. Pure Appl. Math. 57, No. 11, 1413--1457 (2004; Zbl 1077.65055)]. Roughly speaking, the interactive soft shrinkage method is a modified gradient descent one used for sparsity constraints. In the reconstruction, the authors make use of an adaptively selected step size and a smoothing gradient technique. The sparsity reconstruction approach is evaluated by experimental data from water tank measurements.
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