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Iterative Algorithms for Coupled Physics Electrical Conductivity Imaging

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Book cover Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

Coupled Physics Electrical Conductivity Imaging is a group of new imaging modalities in which the electrical conductivity is recovered from the interior data. In this talk the inverse conductivity problem of Current Density Impedance Imaging (CDII) is considered. The variational approach is applied to solve this problem, and the corresponding weighted least gradient problems are analyzed for the Dirichlet and Robin boundary conditions. Three iterative algorithms for constructing the minimizing sequences for the weighted gradient functionals are presented. Their computational effectiveness is demonstrated in numerical experiments. The presentation is based on some results of a long-term project that has been pursued in collaboration with A. Nachman (University of Toronto, Canada) and A. Tamasan (University of Central Florida, USA).

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References

  1. Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    Article  MathSciNet  Google Scholar 

  2. Jerrard, R.L., Moradifam, A., Nachman, A.: Existence and uniqueness of minimizers of general least gradient problems. J. Reine Angew. Math. 734, 71–97 (2018)

    Article  MathSciNet  Google Scholar 

  3. Montalto, C., Stefanov, P.: Stability of coupled physics inverse problems with one internal measurement. Inverse Prob. 29(12), 125004 (2013)

    Article  MathSciNet  Google Scholar 

  4. Montalto, C., Tamasan, A.: Stability in conductivity imaging from partial measurements of one interior current. Inverse Prob. Imaging 11(2), 339–353 (2017)

    Article  MathSciNet  Google Scholar 

  5. Moradifam, A., Nachman, A., Timonov, A.: A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data. Inverse Prob. 28, 084003 (2012)

    Article  MathSciNet  Google Scholar 

  6. Moradifam, A., Nachman, A., Tamasan, A.: Uniqueness of minimizers of weighted least gradient problems arising in conductivity imaging. arXiv:1404.05992 (2017)

  7. Nachman, A., Tamasan, A., Timonov, A.: Conductivity imaging with a single measurement of boundary and interior data. Inverse Prob. 23, 2551–2563 (2007)

    Article  MathSciNet  Google Scholar 

  8. Nachman, A., Tamasan, A., Timonov, A.: Recovering the conductivity from a single measurement of interior data. Inverse Prob. 25, 035014 (2009)

    Article  MathSciNet  Google Scholar 

  9. Nachman, A., Tamasan, A., Timonov, A.: Reconstruction of planar conductivities in subdomains from incomplete data. SIAM J. Appl. Math. 70(8), 3342–3362 (2010)

    Article  MathSciNet  Google Scholar 

  10. Nachman, A., Tamasan, A., Timonov, A.: Current density impedance imaging. Contemp. Math. AMS 559, 1335–1351 (2011)

    MathSciNet  MATH  Google Scholar 

  11. Nachman, A., Tamasan, A., Veras, J.: A weighted minimum gradient problem with complete electrode model boundary conditions for conductivity imaging. SIAM J. Appl. Math. 76(4), 1321–1343 (2016)

    Article  MathSciNet  Google Scholar 

  12. Nashed, Z., Tamasan, A.: Structural stability in a minimization problem and applications to conductivity imaging. Inverse Prob. Imaging 5, 219–236 (2010)

    Article  MathSciNet  Google Scholar 

  13. Nieminen, J.O., Zevenhoven, K.C.J., Vesanen, P.T., et al.: Current density imaging using ultra low field MRI with adiabatic pulses. Magn. Reson. Imaging 32, 54–59 (2014)

    Article  Google Scholar 

  14. Somersalo, E., Cheney, M., Isaacson, D.: Existence and uniqueness for electrode models for electric current computed tomography. SIAM J. Appl. Math. 54(1), 1023–1040 (1992)

    Article  MathSciNet  Google Scholar 

  15. Tamasan, A. and Timonov, A.: A regularized weighted least gradient problem for conductivity imaging. arXiv:1804.00724 (2018)

  16. Tamasan, A., Timonov, A.: Coupled physics electrical conductivity imaging. Eurasian J. Math. Comput. Appl. 2(2), 5–29 (2014)

    Google Scholar 

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Authors and Affiliations

  1. University of South Carolina Upstate, Spartanburg, SC, 29303, USA

    Alex Timonov

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  1. Alex Timonov
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Correspondence to Alex Timonov .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Timonov, A. (2019). Iterative Algorithms for Coupled Physics Electrical Conductivity Imaging. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_63

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_63

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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