Sparsity reconstruction in electrical impedance tomography: an experimental evaluation
type: Item
instance of: scholarly article
title: Sparsity reconstruction in electrical impedance tomography: an experimental evaluation
zbMATH Open document ID: 1251.78008
author: Matthias Gehre
author: Tobias Kluth
author: Antti Lipponen
author: Bangti Jin
author: A. Seppänen
author: Jari P. Kaipio
author: Peter Maass
published in: Journal of Computational and Applied Mathematics
publication date: 2012-04-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 65J22
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 49N45
zbMATH DE Number: 6027505
zbMATH Keywords: electrical impedance tomography
zbMATH Keywords: sparsity reconstruction
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: inverse problem
Wikidata QID: Q59863877
MaRDI profile type: Publication
full work available at URL: j.cam.2011.09.035
OpenAlex ID: W1994097344
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DOI: 10.1016/J.CAM.2011.09.035
description: scientific article