Abstract
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.
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References
A. Allers and F. Santosa, Stability and resolution analysis of a linearized problem in electrical impedance tomography, Inverse Problems, 7 (1991), pp. 515–533.
D. Barber, B. Brown, and J. Jossinet, Electrical impedance tomography, Clinical Physics and Physiological Measurements, 9 (1988). Supplement A.
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.
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).
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.
T. F. Chan, H. M. Zhou, and R. H. Chan, A Continuation Method for Total Variation Denoising Problems, UCLA CAM Report 95-18.
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.
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.
T. Coleman and Y. Li, A globally and quadratically convergent affine scaling method for linear l1problems, Mathematical Programming, 56 (1992), pp. 189–222.
T. Coleman and J. Liu, An interior Newton method for quadratic programming, Cornell University Department of Computer Science Preprint TR 93-1388, 1993.
D. Dobson, Estimates on resolution and stabilization for the linearized inverse conductivity problem, Inverse Problems, 8 (1992), pp. 71–81.
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.
D. Dobson and F. Santosa, An image-enhancement technique for electrical impedance tomography, Inverse Problems 10 (1994) pp. 317–334.
D. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., to appear.
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.
D. Donoho, Superresolution via sparsity constraints, SIAM J. Math. Anal., 23 (1992), pp. 1309–1331.
D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Proc., vol. 4 (1995), pp. 932–945.
E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhauser, Boston, 1984. Monographs in Mathematics, Vol. 80.
G. Golub and C. V. Loan, Matrix Computations, Johns Hopkins, 1983.
K. Ito and K. Kunisch, An active set strategy based on the augmented Lagrangian formulation for image restoration, preprint (1995).
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.
S. Osher and L.I. Rudin, Feature-oriented image enhancement using shock filters, SIAM J. Numer. Anal., 27 (1990), pp. 919–940.
L.I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D., 60 (1992), pp. 259–268.
L.I. Rudin, S. Osher, and C. Fu, Total variation based restoration of noisy blurred images, SIAM J. Num. Anal., to appear.
F. Santosa and W. Symes, Linear inversion of band-limited reflection seismograms, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 1307–1330.
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.
C.R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput., to appear.
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.
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© 1997 Springer-Verlag Wien
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Dobson, D.C. (1997). Recovery of Blocky Images in Electrical Impedance Tomography. In: Engl, H.W., Louis, A.K., Rundell, W. (eds) Inverse Problems in Medical Imaging and Nondestructive Testing. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6521-8_5
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DOI: https://doi.org/10.1007/978-3-7091-6521-8_5
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