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Erschienen in:
Linear Inverse Problems Kapitel lesen Erstes Kapitel lesen

2011 | OriginalPaper | Buchkapitel

Electrical Impedance Tomography

verfasst von : Andy Adler, Romina Gaburro, William Lionheart

Erschienen in: Handbook of Mathematical Methods in Imaging

Verlag: Springer New York

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Electrical Impedance Tomography (EIT) is the recovery of the conductivity (or conductivity and permittivity) of the interior of a body from a knowledge of currents and voltages applied to its surface. In geophysics, where the method is used in prospecting and archaeology, it is known as electrical resistivity tomography. In industrial process tomography it is known as electrical resistance tomography or electrical capacitance tomography. In medical imaging, when at the time of writing it is still an experimental technique rather than routine clinical practice, it is called EIT. A very similar technique is used by weakly electric fish to navigate and locate prey and in this context it is called electrosensing. …

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Vorheriges Kapitel Inverse Scattering
Nächstes Kapitel Synthetic Aperture Radar Imaging
Literatur
1.
Adler A, Lionheart WRB (2006) Uses and abuses of EIDORS: an extensible software base for EIT. Physiol Meas 27:S25–S42CrossRef
2.
3.
Alessandrini G (1990) Singular solutions of elliptic equations and the determination of conductivity by boundary measurements. J Differ Equations 84(2):252–272MathSciNetMATHCrossRef
4.
Alessandrini G (1991) Determining conductivity by boundary measurements, the stability issue. In: Spigler R (ed) Applied and industrial mathematics. Kluwer, Dordrecht, pp 317–324CrossRef
5.
6.
Alessandrini G, Gaburro R (2001) Determining Conductivity with Special Anisotropy by Boundary Measurements. SIAM J Math Anal 33:153–171MathSciNetMATHCrossRef
7.
Alessandrini G, Gaburro R (2009) The local Calderón problem and the determination at the boundary of the conductivity. Commun Part Differ Eq 34:918–936MathSciNetMATHCrossRef
8.
9.
Ammari H, Buffa A, Nédélec J-C (2000) A justification of eddy currents model for the Maxwell equations. SIAM J Appl Math 60: 1805–1823MathSciNetMATHCrossRef
10.
Aronszajn N (1957) A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J Math Pures Appl 36:235–249MathSciNetMATH
11.
12.
Barber D, Brown B (1986) Recent developments in applied potential tomography – APT. In: Bacharach SL (ed) Information processing in medical imaging. Nijhoff, Amsterdam, pp 106–121CrossRef
13.
Barceló JA, Faraco D, Ruiz A (2001) Stability of the inverse problem in the plane for less regular conductivities. J Differ Equations 173:231–270MATHCrossRef
14.
Barceló JA, Barceló T, Ruiz A (2007) Stability of Calderón inverse conductivity problem in the plane. J Math Pures Appl 88:522–556MathSciNetMATHCrossRef
15.
Berenstein CA, Casadio Tarabusi E (1996) Integral geometry in hyperbolic spaces and electrical impedance tomography. SIAM J Appl Math 56:75564MathSciNetCrossRef
16.
Bikowski J (2009) Electrical impedance tomography reconstructions in two and three dimensions; from Calderón to direct methods. PhD thesis, Colorado State University, Fort Collins
17.
Borcea L (2002) Electrical impedance tomography. Inverse Prob 18:R99–R136; Borcea L (2003) Addendum to electrical impedance tomography. Inverse Prob 19:997–998
18.
Borsic A, Graham BM, Adler A, Lionheart WRB (2010) Total variation regularization in electrical impedance tomography. IEEE Trans Med Imaging 29(1):44–54CrossRef
19.
Brown R (2001) Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result. J Inverse Ill-Posed Prob 9:567–574MATH
20.
Beals R, Coifman R (1982) Transformation spectrales et equation d’evolution non lineares. Seminaire Goulaouic-Meyer-Schwarz, exp 9, pp 1981–1982
21.
Beals R, Coifman RR (1989) Linear spectral problems, non-linear equations and the \(\bar{\partial }\)-method. Inverse Prob 5:87130MathSciNetCrossRef
22.
Brown R, Torres R (2003) Uniqueness in the inverse conductivity problem for conductivities with 3 ∕ 2 derivatives in L p , p > 2n. J Fourier Anal Appl 9:1049–1056MathSciNetCrossRef
23.
Brown R, Uhlmann G (1997) Uniqueness in the inverse conductivity problem with less regular conductivities in two dimensions. Commun Part Differ Eq 22:1009–1027MathSciNetMATHCrossRef
24.
25.
Calderón AP (1980) On an inverse boundary value problem. In: Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980). Soc Brasil Mat, Rio de Janeiro, pp 65–73
26.
Calderón AP (2006) On an inverse boundary value problem. Comput Appl Math 25(2–3):133–138 (Note this reprint has some different typographical errors from the original: in particular on the first page the Dirichlet data for w is φ not zero)
27.
Chambers JE, Meldrum PI, Ogilvy RD, Wilkinson PB (2005) Characterisation of a NAPL-contaminated former quarry site using electrical impedance tomography. Near Surface Geophysics 3:79–90
28.
Chambers JE, Kuras O, Meldrum PI, Ogilvy RD, Hollands J (2006) Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site. Geophysics 71:B231–B239CrossRef
29.
Cheng K, Isaacson D, Newell JC, Gisser DG (1989) Electrode models for electric current computed tomography. IEEE Trans Biomed Eng 36:918–924CrossRef
30.
31.
Cornean H, Knudsen K, Siltanen S (2006) Towards a D-bar reconstruction method for three dimensional EIT. J Inverse Ill-Posed Prob 14:111134MathSciNet
32.
33.
Di Cristo M (2007) Stable determination of an inhomogeneous inclusion by local boundary measurements. J Comput Appl Math 198:414–425MathSciNetMATHCrossRef
34.
Ciulli S, Ispas S, Pidcock MK (1996) Anomalous thresholds and edge singularities in electrical impedance tomography. J Math Phys 37:4388MathSciNetMATHCrossRef
35.
Dobson DC (1990) Stability and regularity of an inverse elliptic boundary value problem. Technical report TR90-14, Rice University, Department of Mathematical Sciences
36.
Doerstling BH (1995) A 3-d reconstruction algorithm for the linearized inverse boundary value problem for Maxwell’s equations. PhD thesis, Rensselaer Polytechnic Institute, Troy
37.
Druskin V (1982) The unique solution of the inverse problem of electrical surveying and electrical well-logging for piecewise-constant conductivity. Izv Phys Solid Earth 18:51–53 (in Russian)
38.
Druskin V (1985) On uniqueness of the determination of the three-dimensional underground structures from surface measurements with variously positioned steady-state or monochromatic field sources. Sov Phys Solid Earth 21:210–214 (in Russian)
39.
40.
Gaburro R (1999) Sul Problema Inverso della Tomografia da Impedenza Elettrica nel Caso di Conduttivitá Anisotropa. Tesi di Laurea in Matematica, Universitá degli Studi di Trieste
41.
Gaburro R (2003) Anisotropic conductivity. Inverse boundary value problems. PhD thesis, University of Manchester Institute of Science and Technology (UMIST), Manchester
42.
Gaburro R, Lionheart WRB (2009) Recovering Riemannian metrics in monotone families from boundary data. Inverse Prob 25:045004 (14pp)
43.
Geotomo Software (2009) RES3DINV ver 2.16, Rapid 3D resistivity and IP inversion using the least-squares method. Geotomo Software, Malaysia. www.​geoelectrical.​com
44.
Gisser DG, Isaacson D, Newell JC (1990) Electric current computed tomography and eigenvalues. SIAM J Appl Math 50:1623–1634MathSciNetMATHCrossRef
45.
Griffiths H, Jossinet J (1994) Bioelectric tissue spectroscopy from multifrequency EIT. Physiol Meas 15(2A):29–35
46.
Griffiths H (2001) Magnetic induction tomography. Meas Sci Technol 12:1126–1131CrossRef
47.
Hanke M (2008) On real-time algorithms for the location search of discontinuous conductivities with one measurement. Inverse Prob 24:045005MathSciNetCrossRef
48.
Hanke M, Schappel B (2008) The factorization method for electrical impedance tomography in the half-space. SIAM J Appl Math 68:907–924MathSciNetMATHCrossRef
49.
Hähner P (1996) A periodic Faddeev-type solution operator. J Differ Equations 128: 300–308MATHCrossRef
50.
Huang SM, Plaskowski A, Xie CG, Beck MS (1988) Capacitance-based tomographic flow imaging system. Electronics Lett 24:418–419CrossRef
51.
Heck H, Wang J-N, (2006) Stability estimates for the inverse boundary value problem by partial Cauchy data. Inverse Prob 22:1787–1796MathSciNetMATHCrossRef
52.
Heikkinen LM, Vilhunen T, West RM, Vauhkonen M (2002) Simultaneous reconstruction of electrode contact impedances and internal electrical properties: II. Laboratory experiments. Meas Sci Technol 13:1855CrossRef
53.
Henderson RP, Webster JG (1978) An Impedance camera for spatially specific measurements of the thorax. IEEE Trans Biomed Eng BME-25(3):250–254
54.
Holder DS (2005) Electrical impedance tomography methods history and applications. Institute of Physics, Bristol
55.
Ikehata M (2001) The enclosure method and its applications, chapter 7. In: Analytic extension formulas and their applications (Fukuoka, 1999/Kyoto, 2000). Kluwer; Int Soc Anal Appl Comput 9:87–103MathSciNet
56.
Ikehata M, Siltanen S (2000) Numerical method for nding the convex hull of an inclusion in conductivity from boundary measurements. Inverse Prob 16:273–296MathSciNet
57.
Ingerman D, Morrow JA (1998) On a characterization of the kernel of the Dirichlet-to-Neumann map for a planar region. SIAM J Math Anal 29:106115MathSciNetCrossRef
58.
Isaacson D (1986) Distinguishability of conductivities by electric current computed tomography. IEEE TransMed Imaging 5:92–95
59.
Isaacson D, Mueller JL, Newell J, Siltanen S (2004) Reconstructions of chest phantoms by the d-bar method for electrical impedance tomography. IEEE Trans Med Imaging 23:821–828CrossRef
60.
Isaacson D, Mueller JL, Newell J, Siltanen S (2006) Imaging cardiac activity by the D-bar method for electrical impedance tomography. Physiol Meas 27:S43–S50CrossRef
61.
62.
63.
Kaipio J, Kolehmainen V, Somersalo E, Vauhkonen M (2000) Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Inverse Prob 16:1487–1522MathSciNetMATHCrossRef
64.
Kang H, Yun K (2002) Boundary determination of conductivities and Riemannian metrics via local Dirichlet-to-Neumann operator. SIAM J Math Anal 34:719–735MathSciNetCrossRef
65.
Kenig C, Sjöstrand J, Uhlmann G (2007) The Calderón problem with partial data. Ann Math 165:567–591MATHCrossRef
66.
Kim Y, Woo HW (1987) A prototype system and reconstruction algorithms for electrical impedance technique in medical body imaging. Clin Phys Physiol Meas 8:63–70CrossRef
67.
Kohn R, Vogelius M (1984) Identification of an Unknown Conductivity by Means of Measurements at the Boundary. SIAM-AMS Proc 14:113–123MathSciNet
68.
Kohn R, Vogelius M (1985) Determining conductivity by boundary measurements II. Interior results. Comm Pure Appl Math 38: 643–667MathSciNetMATHCrossRef
69.
Knudsen K, Lassas M, Mueller JL, Siltanen S (2009) Regularized D-bar method for the inverse conductivity problem. Inverse Prob Imaging 3:599–624MathSciNetMATHCrossRef
70.
Lassas M, Uhlmann G (2001) Determining a Riemannian manifold from boundary measurements. Ann Sci École Norm Sup 34: 771–787MathSciNetMATH
71.
Lassas M, Taylor M, Uhlmann G (2003) The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary. Commun Geom Anal 11:207–222MathSciNetMATH
72.
73.
Lee JM, Uhlmann G (1989) Determining anisotropic real-analytic conductivities by boundary measurements. Commun Pure Appl Math 42:1097–1112MathSciNetMATHCrossRef
74.
Liu L (1997) Stability estimates for the two-dimensional inverse conductivity problem. PhD thesis, University of Rochester, New York
75.
76.
Loke MH, Barker RD (1996) Rapid least- squares inversion by a quasi- Newton method. Geophys Prospect 44:131152
77.
Loke MH, Chambers JE, Ogilvy RD (2006) Inversion of 2D spectral induced polarization imaging data. Geophys Prospect 54: 287–301CrossRef
78.
79.
Meyers NG (1963) An Lp estimate for the gradient of solutions of second order elliptic divergence equations. Ann Scuola Norm Sup-Pisa 17(3):189–206MathSciNetMATH
80.
Molinari M, Blott BH, Cox SJ, Daniell GJ (2002) Optimal imaging with adaptive mesh refinement in electrical tomography. Physiol Meas 23(1):121–128CrossRef
81.
82.
83.
Nachman A, Sylvester J, Uhlmann G (1988) An n-dimensional Borg-Levinson theorem. Commun Math Phys 115:593–605MathSciNetCrossRef
84.
Nakamura G, Tanuma K (2001) Local determination of conductivity at the boundary from the Dirichlet-to-Neumann map. Inverse Prob 17:405–419MathSciNetMATHCrossRef
85.
Nakamura G, Tanuma K (2001) Direct determination of the derivatives of conductivity at the boundary from the localized Dirichlet to Neumann map. Commun Korean Math Soc 16:415–425MathSciNetMATH
86.
Nakamura G, Tanuma K (2003) Formulas for reconstrucing conductivity and its normal derivative at the boundary from the localized Dirichlet to Neumann map. In: Hon Y-C, Yamamoto M, Cheng J, Lee J-Y (eds) Proceeding international conference on inverse problem-recent development in theories and numerics. World Scientific, River Edge, pp 192–201CrossRef
87.
Novikov RG (1988) A multidimensional inverse spectral problem for the equation \(-\Delta \psi + (v(x) - Eu(x))\psi \,=\,0\). (Russian) Funktsional. Anal i Prilozhen 22, 4:11–22, 96; translation in Funct Anal Appl 22, 4:263–272 (1989)
88.
Paulson K, Breckon W, Pidcock M (1992) Electrode modeling in electrical-impedance tomography. SIAM J Appl Math 52:1012–1022MATHCrossRef
89.
Päivärinta L, Panchenko A, Uhlmann G (2003) Complex geometrical optics solutions for Lipschitz conductivities. Rev Mat Iberoam 19: 57–72MATHCrossRef
90.
Polydorides N, Lionheart WRB (2002) A Matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the electrical impedance and diffuse optical reconstruction software project. Meas Sci Technol 13:1871–1883CrossRef
91.
Seagar AD (1983) Probing with low frequency electric current. PhD thesis, University of Canterbury, Christchurch
92.
Seagar AD, Bates RHT (1985) Full-wave computed tomography. Pt 4: Low-frequency electric current CT. Inst Electr Eng Proc Pt A 132:455–466
93.
Siltanen S, Mueller JL, Isaacson D (2000) An implementation of the reconstruction algorithm of A. Nachman for the 2-D inverse conductivity problem. Inverse Prob 16:681–699MathSciNetMATHCrossRef
94.
Soleimani M, Lionheart WRB (2005) Nonlinear image reconstruction for electrical capacitance tomography experimental data using. Meas Sci Technol 16(10):1987–1996CrossRef
95.
Soleimani M, Lionheart WRB, Dorn O (2006) Level set reconstruction of conductivity and permittivity from boundary electrical measurements using expeimental data. Inverse Prob Sci Eng 14:193–210MATHCrossRef
96.
Somersalo E, Cheney M, Isaacson D (1992) Existence and uniqueness for electrode models for electric current computed tomography. SIAM J Appl Math 52:1023–1040MathSciNetMATHCrossRef
97.
Soni NK (2005) Breast imaging using electrical impedance tomography. PhD thesis, Dartmouth College, NH
98.
99.
Sylvester J, Uhlmann G (1986) A uniqueness theorem for an inverse boundary value problem in electrical prospection. Commun Pure Appl Math 39:92–112MathSciNetCrossRef
100.
101.
Sylvester J, Uhlmann G (1988) Inverse boundary value problems at the boundary – continuous dependence. Commun Pure Appl Math 41:197–221MathSciNetCrossRef
102.
Tamburrino A, Rubinacci G (2002) A new non-iterative inversion method for electrical resistance tomography. Inverse Prob 18: 1809–1829MathSciNetMATHCrossRef
103.
Uhlmann G (2009) Topical review: electrical impedance tomography and Calderón’s problem. Inverse Prob 25:123011 (39pp)
104.
Vauhkonen M, Lionheart WRB, Heikkinen LM, Vauhkonen PJ, Kaipio JP (2001) A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images. Physiol Meas 22:107–111CrossRef
105.
Vauhkonen M (1997) Electrical impedance tomography and prior information. PhD thesis, University of Kuopio, Kuopio
106.
Vauhkonen M, Karjalainen PA, Kaipio JP (1998) A Kalman Filter approach to track fast impedance changes in electrical impedance tomography. IEEE Trans Biomed Eng 45:486–493CrossRef
107.
West RM, Soleimani M, Aykroyd RG, Lionheart WRB (2006) Speed Improvement of MCMC Image Reconstruction in Tomography by Partial Linearization. Int J Tomogr Stat 4, No. S06: 13–23MathSciNet
108.
West RM, Jia X, Williams RA (2000) Parametric modelling in industrial process tomography. Chem Eng J 77:31–36CrossRef
109.
Yang WQ, Spink DM, York TA, McCann H (1999) An image reconstruction algorithm based on Landwebers iteration method for electrical-capacitance tomography. Meas Sci Technol 10:1065–1069CrossRef
110.
York T (2001) Status of electrical tomography in industrial applications. J Electron Imaging 10:608–619CrossRef
Metadaten
Titel
Electrical Impedance Tomography
verfasst von
Andy Adler
Romina Gaburro
William Lionheart
Copyright-Jahr
2011
Verlag
Springer New York
Buch
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-0-387-92919-4

Electronic ISBN: 978-0-387-92920-0

Copyright-Jahr: 2011

DOI
https://doi.org/10.1007/978-0-387-92920-0_14

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