A reconstruction algorithm for electrical impedance tomography based on sparsity regularization
KAUST Grant NumberKUS-C1-016-04
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AbstractThis paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the 'inhomogeneity' with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity-promoting ℓ 1-penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two-dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization. © 2011 John Wiley & Sons, Ltd.
CitationJin B, Khan T, Maass P (2011) A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. Int J Numer Meth Engng 89: 337–353. Available: http://dx.doi.org/10.1002/nme.3247.
SponsorsThe authors are grateful to two anonymous referees for their constructive comments that have led to a significant improvement in the presentation of the manuscript. The first author was substantially supported by the Alexander von Humboldt Foundation through a postdoctoral researcher fellowship and was partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The second author thanks the US National Science Foundation for supporting the work on this project by grant DMS 0915214, and the third author would like to thank the German Science Foundation for supporting the work through grant MA 1657/18-1.