August  2012, 6(3): 399-421. doi: 10.3934/ipi.2012.6.399

Fine-tuning electrode information in electrical impedance tomography

1. 

Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland, Finland, Finland, Finland

Received  July 2011 Revised  May 2012 Published  September 2012

Electrical impedance tomography is a noninvasive imaging technique for recovering the admittivity distribution inside a body from boundary measurements of current and voltage. In practice, impedance tomography suffers from inaccurate modelling of the measurement setting: The exact electrode locations and the shape of the imaged object are not necessarily known precisely. In this work, we tackle the problem with imperfect electrode information by introducing the Fréchet derivative of the boundary measurement map of impedance tomography with respect to the electrode shapes and locations. This enables us to include the fine-tuning of the information on the electrode positions as a part of a Newton-type output least squares reconstruction algorithm; we demonstrate that this approach is feasible via a two-dimensional numerical example based on simulated data. The impedance tomography measurements are modelled by the complete electrode model, which is in good agreement with real-life electrode measurements.
Citation: Jérémi Dardé, Harri Hakula, Nuutti Hyvönen, Stratos Staboulis. Fine-tuning electrode information in electrical impedance tomography. Inverse Problems & Imaging, 2012, 6 (3) : 399-421. doi: 10.3934/ipi.2012.6.399
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show all references

References:
[1]

Clin. Phys. Physiol. Meas., 9 (1988), 101-104. Google Scholar

[2]

Inverse Problems, 18 (2002), R99-R136. doi: 10.1088/0266-5611/18/6/201.  Google Scholar

[3]

Clin. Phys. Physiol. Meas., 9 (1988), 105-109. Google Scholar

[4]

SIAM Rev., 41 (1999), 85-101. doi: 10.1137/S0036144598333613.  Google Scholar

[5]

IEEE Trans. Biomed. Eng., 36 (1989), 918-924. doi: 10.1109/10.35300.  Google Scholar

[6]

Wiley, New York, 1983.  Google Scholar

[7]

Springer-Verlag, Berlin, 1992.  Google Scholar

[8]

J. Dardé, N. Hyvönen, A. Seppänen and S. Staboulis, Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography,, submitted., ().   Google Scholar

[9]

Vol. 2, Springer-Verlag, Berlin, 1988.  Google Scholar

[10]

SIAM, Philadelphia, 2001.  Google Scholar

[11]

Inverse Problems, 27 (2011), 115008. doi: 10.1088/0266-5611/27/11/115008.  Google Scholar

[12]

Math. Models Methods Appl. Sci., 21 (2011), 1395-1413. doi: 10.1142/S0218202511005362.  Google Scholar

[13]

Meas. Sci. Technol., 13 (2002), 1855-1861. doi: 10.1088/0957-0233/13/12/308.  Google Scholar

[14]

Inverse Problems, 11 (1995), 371-382. doi: 10.1088/0266-5611/11/2/007.  Google Scholar

[15]

Inverse Problems, 14 (1998), 209-210. doi: 10.1088/0266-5611/14/1/017.  Google Scholar

[16]

Inverse Problems, 14 (1998), 67-82. doi: 10.1088/0266-5611/14/1/008.  Google Scholar

[17]

in "Large-scale Inverse Problems and Quantification of Uncertainty'' (eds. L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. Van Bloemen Waanders and K. Willcox), Wiley, Chichester, 2011.  Google Scholar

[18]

SIAM J. Appl. Math, 64 (2004), 902-931. doi: 10.1137/S0036139903423303.  Google Scholar

[19]

Inverse Problems, 23 (2007), 2249-2270. doi: 10.1088/0266-5611/23/5/026.  Google Scholar

[20]

SIAM J. Appl. Math, 70 (2010), 1878-1898. doi: 10.1137/09075929X.  Google Scholar

[21]

Inverse Problems, 16 (2000), 1487-1522. doi: 10.1088/0266-5611/16/5/321.  Google Scholar

[22]

Springer-Verlag, New York, 2005.  Google Scholar

[23]

Inverse Problems, 9 (1993), 81-96.  Google Scholar

[24]

SIAM J. Appl. Math, 66 (2005), 365-383. doi: 10.1137/040612737.  Google Scholar

[25]

Physiol. Meas., 18 (1997), 289-303. Google Scholar

[26]

Inverse Problems, 22 (2006), 1967-1987. doi: 10.1088/0266-5611/22/6/004.  Google Scholar

[27]

Inverse Problems, 24 (2008), 065009. doi: 10.1088/0266-5611/24/6/065009.  Google Scholar

[28]

\textbfI, Springer-Verlag, New York-Heidelberg, 1972.  Google Scholar

[29]

Meas. Sci. Technol., 19 (2008), 015501. doi: 10.1088/0957-0233/19/1/015501.  Google Scholar

[30]

Meas. Sci. Technol., 20 (2009), 105504. doi: 10.1088/0957-0233/20/10/105504.  Google Scholar

[31]

IEEE Trans. Med. Imag., 30 (2011), 231-242. doi: 10.1109/TMI.2010.2073716.  Google Scholar

[32]

Springer-Verlag, New York, 1999.  Google Scholar

[33]

Physiol. Meas., 27 (2006), S103-S113. doi: 10.1088/0967-3334/27/5/S09.  Google Scholar

[34]

SIAM J. Appl. Math., 52 (1992), 1023-1040. doi: 10.1137/0152060.  Google Scholar

[35]

Inverse Problems, 25 (2009), 123011. doi: 10.1088/0266-5611/25/12/123011.  Google Scholar

[36]

Meas. Sci. Technol., 13 (2002), 1848-1854. doi: 10.1088/0957-0233/13/12/307.  Google Scholar

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