Fast, non-linear inversion for Electrical Impedance Tomography

  • Kevin Paulson
  • William Lionheart
  • Michael Pidcock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 687)


Electrical Impedance Tomography, (EIT), is a non-invasive imaging technique which aims to image the impedance within a test volume from electrical measurements made on the surface. The reconstruction of impedance images is an ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. This paper defines an experimental measurement in EIT and calculates optimal experiments which maximise the distinguishability between the region to be imaged and a best estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. A reconstruction algorithm, known as POMPUS, based on the use of optimal experiments is derived. It is proved to converge given some mild constraints and is demonstrated to be many times faster than standard, Newton based, reconstruction algorithms. Results using synthetic data indicate that the images produced by POMPUS are comparable to those produced by these standard algorithms.


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  1. 1.
    D.C.Barber,B. Brown: Recent Developments in Applied Potential Tomography-APT. In: S. L. Bacharach, M. Nijhoff (eds): Information Processing in Medical Imaging, Martinus Nijhoff 1986, pp 106–121Google Scholar
  2. 2.
    D.C.Barber,B. Brown: Reconstruction of Impedance Images using Filtered Back-Projection. In: Proceedings of a European Community Meeting on Electrical Impedance Tomography, Copenhagen 1990, pp 1–8Google Scholar
  3. 3.
    W.R. Breckon, M.K. Pidcock: Some Mathematical Aspects of Electrical Impedance Tomography. In: M.A. Viergever, A.E. Todd-Pokropek (eds): Mathematics and Computer Science in Medical Imaging, NATO ASI Series, Vol F39, Springer-Verlag Berlin Heidelberg 1988,pp 351–362Google Scholar
  4. 4.
    W.R.Breckon, M.K. Pidcock: Data Errors and Reconstruction Algorithms in Electrical Impedance Tomography. Clin.l Phys Physiol. Meas., Vol 9, Suppl. A 1988, pp 51–58Google Scholar
  5. 5.
    W.R.Breckon: Image Reconstruction in Electrical Impedance Tomography, PhD Thesis, Oxford Polytechnic, May 1990Google Scholar
  6. 6.
    K. Cheng, D. Isaacson, J. Newell, D. Gisser: Electrode Models for Electric Current Computed Tomography., IEEE Transactions on Biomedical Engineering Vol 36, No. 9 1989, pp 918–924CrossRefPubMedGoogle Scholar
  7. 7.
    R. Fletcher: Practical Methods of Optimisation, 2nd Edition, Wiley, 1987Google Scholar
  8. 8.
    G. Folland: Introduction to Partial Differential Equations, Princeton University Press, New Jersey, 1976Google Scholar
  9. 9.
    G. Golub, C. Van Loan: Matrix Computations, The John Hopkins University Press, 1983Google Scholar
  10. 10.
    C. Groetsch: The Theory of Tikhonov Regularisation forFredholm Equations of the First Kind, Research Notes in Mathematics, Pitman Advanced Publishing Program, London, 1984.Google Scholar
  11. 11.
    R. Horn,C. Johnson: Matrix Analysis. Cambridge University Press, 1985Google Scholar
  12. 12.
    D. Isaacson: Distinguishabilities of Conductivities by Electric Current Computed Tomography. IEEE Trans. Medical Imaging, vol MI-5, no. 6 1986, pp 91–95Google Scholar
  13. 13.
    F. Natterer: The Mathematics of Computerized Tomography, Wiley 1986.Google Scholar
  14. 14.
    K.S. Paulson, W.R. Breckon, M.K. Pidcock: Electrode Modelling in Electrical Impedance Tomography, SIAM Journal on Applied Maths., vol. 52, Issue 4., August 1992Google Scholar
  15. 15.
    See, for example, Clin. Phys. Physiol. Meas., vol. 13, Suppl. A.1992Google Scholar
  16. 16.
    Proceedings of a meeting of the European Concerted Action on Process Tomography(ECAPT), Manchester, England 1992Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Kevin Paulson
    • 1
  • William Lionheart
    • 1
  • Michael Pidcock
    • 1
  1. 1.School of Computing and Mathematical SciencesOxford Brookes UniversityOxfordUK

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