Recovery of Blocky Images in Electrical Impedance Tomography

  • David C. Dobson


The techniques of electrical impedance tomography (EIT) have been widely studied over the past several years, for applications in both medical imaging and nondestructive evaluation. The goal is to find the electrical conductivity of a spatially inhomogeneous medium inside a given domain, using electrostatic measurements collected at the boundary.


Total Variation Singular Value Decomposition Electrical Impedance Tomography Current Pattern Total Variation Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Allers and F. Santosa, Stability and resolution analysis of a linearized problem in electrical impedance tomography, Inverse Problems, 7 (1991), pp. 515–533.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    D. Barber, B. Brown, and J. Jossinet, Electrical impedance tomography, Clinical Physics and Physiological Measurements, 9 (1988). Supplement A.Google Scholar
  3. 3.
    W.R. Breckon and M.K. Pidcock, Some mathematical aspects of electrical impedance tomography, in Mathematics and Computer Science in Medical Imaging, M.A. Viergever and A. Todd-Pokropek, eds., NATO ASI Series, Springer Verlag (1987), pp. 351–362.Google Scholar
  4. 4.
    A.P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics (Soc. Brasileira de Matematica, Rio de Janerio (1980).Google Scholar
  5. 5.
    F. Catte, P.L. Lions, J. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29 (1992), pp. 182–193.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    T. F. Chan, H. M. Zhou, and R. H. Chan, A Continuation Method for Total Variation Denoising Problems, UCLA CAM Report 95-18.Google Scholar
  7. 7.
    A. Chambolle and P. L. Lions, Image recovery via total variation minimization and related problems, Research Report No. 9509, CEREMADE, Universite de Paris-Dauphine, 1995.Google Scholar
  8. 8.
    P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, Deterministic edge-preserving regularization in computed imaging, Research Report no. 94-01, Univ. of Nice-Sophia Antipolis, 1994.Google Scholar
  9. 9.
    T. Coleman and Y. Li, A globally and quadratically convergent affine scaling method for linear l1problems, Mathematical Programming, 56 (1992), pp. 189–222.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    T. Coleman and J. Liu, An interior Newton method for quadratic programming, Cornell University Department of Computer Science Preprint TR 93-1388, 1993.Google Scholar
  11. 11.
    D. Dobson, Estimates on resolution and stabilization for the linearized inverse conductivity problem, Inverse Problems, 8 (1992), pp. 71–81.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    D. Dobson, Exploiting ill-posedness in the design of diffractive optical structures, in “Mathematics in Smart Structures”, H. T. Banks, ed., SPIE Proc. 1919 (1993), pp. 248–257.Google Scholar
  13. 13.
    D. Dobson and F. Santosa, An image-enhancement technique for electrical impedance tomography, Inverse Problems 10 (1994) pp. 317–334.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    D. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., to appear.Google Scholar
  15. 15.
    D. Dobson and F. Santosa, Resolution and stability analysis of an inverse problem in electrical impedance tomography—dependence on the input current patterns. SIAM J. Appl. Math, 54 (1994) pp. 1542–1560.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    D. Donoho, Superresolution via sparsity constraints, SIAM J. Math. Anal., 23 (1992), pp. 1309–1331.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Proc., vol. 4 (1995), pp. 932–945.CrossRefGoogle Scholar
  18. 18.
    E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhauser, Boston, 1984. Monographs in Mathematics, Vol. 80.Google Scholar
  19. 19.
    G. Golub and C. V. Loan, Matrix Computations, Johns Hopkins, 1983.Google Scholar
  20. 20.
    K. Ito and K. Kunisch, An active set strategy based on the augmented Lagrangian formulation for image restoration, preprint (1995).Google Scholar
  21. 21.
    Y. Li and F. Santosa, An affine scaling algorithm for minimizing total variation in image enhancement, Cornell Theory Center Technical Report 12/94, submitted to IEEE Trans. Image Proc.Google Scholar
  22. 22.
    S. Osher and L.I. Rudin, Feature-oriented image enhancement using shock filters, SIAM J. Numer. Anal., 27 (1990), pp. 919–940.MATHCrossRefGoogle Scholar
  23. 23.
    L.I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D., 60 (1992), pp. 259–268.MATHCrossRefGoogle Scholar
  24. 24.
    L.I. Rudin, S. Osher, and C. Fu, Total variation based restoration of noisy blurred images, SIAM J. Num. Anal., to appear.Google Scholar
  25. 25.
    F. Santosa and W. Symes, Linear inversion of band-limited reflection seismograms, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 1307–1330.MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    F. Santosa and W. Symes, Reconstruction of blocky impedance profiles from normal-incidence reflection seismograms which are band-limited and miscalibrated, Wave Motion, 10 (1988), pp. 209–230.MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    C.R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput., to appear.Google Scholar
  28. 28.
    C.R. Vogel and M. E. Oman, Fast numerical methods for total variation minimization in image reconstruction, in SPIE Proc. Vol. 2563, Advanced Signal Processing Algorithms, July 1995.Google Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • David C. Dobson
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

Personalised recommendations