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A Novel Method for the Numerical Solution of a Hybrid Inverse Problem of Electrical Conductivity Imaging

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A novel method for the numerical solution of a hybrid (coupled physics) inverse problem is proposed. Based on a regularized weighted mean curvature flow equation, this method can be considered as an alternative to the variational approach to solving weighted least gradient Dirichlet problems arising in electrical conductivity imaging, in particular, in Current Density Impedance Imaging (CDII). Utilizing the Sternberg–Ziemer theory, convergence of regularized solutions to a unique function of weighted least gradient is established. The numerical study is conducted to demonstrate the practicability and computational effectiveness of the proposed method.

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Authors and Affiliations

  1. St.Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

    A. Timonov

  2. University of South Carolina (Upstate campus), Columbia, SC, USA

    A. Timonov

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  1. A. Timonov
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Correspondence to A. Timonov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 499, 2021, pp. 105–128.

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Timonov, A. A Novel Method for the Numerical Solution of a Hybrid Inverse Problem of Electrical Conductivity Imaging. J Math Sci 273, 511–526 (2023). https://doi.org/10.1007/s10958-023-06517-8

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