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Volumn 1, Issue 2, 2007, Pages 299-317

Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography

Author keywords

Electrical impedance tomography; Electrode models; Factorization method; Hp FEM; Inclusions; Inverse boundary value problems; Schwarz Christoffel map

Indexed keywords


EID: 84910114486     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2007.1.299     Document Type: Article
Times cited : (38)

References (34)
  • 1
    • 0001666009 scopus 로고
    • Singular solutions of elliptic equations and the determination of conductivity by boundary measurements
    • G. Alessandrini, Singular solutions of elliptic equations and the determination of conductivity by boundary measurements, J. Differential Equations, 84 (1990), 252–272.
    • (1990) J. Differential Equations , vol.84 , pp. 252-272
    • Alessandrini, G.1
  • 2
    • 30444450433 scopus 로고    scopus 로고
    • Calderon’s inverse conductivity problem in the plane
    • K. Astala and L. Päivärinta, Calderon’s inverse conductivity problem in the plane, Ann. of Math., 163 (2006), 265–299.
    • (2006) Ann. of Math. , vol.163 , pp. 265-299
    • Astala, K.1    Päivärinta, L.2
  • 3
    • 13744259841 scopus 로고    scopus 로고
    • Reconstructions in impedance and optical tomography with singular interfaces
    • G. Bal, Reconstructions in impedance and optical tomography with singular interfaces, Inverse Problems, 21 (2005), 113–131.
    • (2005) Inverse Problems , vol.21 , pp. 113-131
    • Bal, G.1
  • 4
    • 0036904346 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • L. Borcea, Electrical impedance tomography, Inverse Problems, 18 (2002), R99–R136.
    • (2002) Inverse Problems , vol.18 , pp. RR99-R136
    • Borcea, L.1
  • 5
    • 0001659228 scopus 로고    scopus 로고
    • Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
    • R. M. Brown and G. Uhlmann, Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions, Comm. Partial Differential Equations, 22 (1997), 1009–1027.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 1009-1027
    • Brown, R.M.1    Uhlmann, G.2
  • 6
    • 0007214756 scopus 로고    scopus 로고
    • Gebietserkennung in der elektrischen Impedanztomographie
    • Uni-versitt Karlsruhe
    • M. Brühl, “Gebietserkennung in der elektrischen Impedanztomographie,” Dissertation, Uni-versitt Karlsruhe, 1999.
    • (1999) Dissertation
    • Brühl, M.1
  • 7
    • 0035541164 scopus 로고    scopus 로고
    • Explicit characterization of inclusions in electrical impedance tomography
    • M. Brühl, Explicit characterization of inclusions in electrical impedance tomography, SIAM J. Math. Anal., 32 (2001), 1327–1341.
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 1327-1341
    • Brühl, M.1
  • 8
    • 0000252505 scopus 로고    scopus 로고
    • Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
    • M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography, Inverse Problems, 16 (2000), 1029–1042.
    • (2000) Inverse Problems , vol.16 , pp. 1029-1042
    • Brühl, M.1    Hanke, M.2
  • 9
    • 0002713385 scopus 로고
    • On an inverse boundary value problem
    • (ed: W. H. Meyer and M. A. Raupp, Rio de Janeiro), 1980, Soc. Brasil. Mat
    • A. P. Calderón, On an inverse boundary value problem, in “Seminar on Numerical Analysis and its Application to Continuum Physics” (ed: W. H. Meyer and M. A. Raupp, Rio de Janeiro), 1980, Soc. Brasil. Mat., 1980, 65–73.
    • (1980) Seminar on Numerical Analysis and Its Application to Continuum Physics , pp. 65-73
    • Calderón, A.P.1
  • 10
  • 11
    • 0030172363 scopus 로고    scopus 로고
    • Algorithm 756; a MATLAB toolbox for Schwarz-Christoffel mapping
    • T. A. Driscoll, Algorithm 756; a MATLAB toolbox for Schwarz-Christoffel mapping, ACM Trans. Math. Soft., 22 (1996), 168–186.
    • (1996) ACM Trans. Math. Soft. , vol.22 , pp. 168-186
    • Driscoll, T.A.1
  • 13
    • 33645137537 scopus 로고    scopus 로고
    • The factorization method for real elliptic problems
    • B. Gebauer, The factorization method for real elliptic problems, Journal for Analysis and its Applications, 25 (2006), 81–102.
    • (2006) Journal for Analysis and Its Applications , vol.25 , pp. 81-102
    • Gebauer, B.1
  • 14
    • 3042686014 scopus 로고    scopus 로고
    • Complete electrode model of electrical impedance tomography: Approximation properties and characterization of inclusions
    • N. Hyvönen, Complete electrode model of electrical impedance tomography: Approximation properties and characterization of inclusions, SIAM J. Appl. Math., 64 (2004), 902–931.
    • (2004) SIAM J. Appl. Math. , vol.64 , pp. 902-931
    • Hyvönen, N.1
  • 15
    • 3042670498 scopus 로고    scopus 로고
    • Characterizing inclusions in optical tomography
    • N. Hyvönen, Characterizing inclusions in optical tomography, Inverse Problems, 20 (2004), 737–751.
    • (2004) Inverse Problems , vol.20 , pp. 737-751
    • Hyvönen, N.1
  • 16
    • 23244432912 scopus 로고    scopus 로고
    • Application of a weaker formulation of the factorization method to the characterization of absorbing inclusions in optical tomography
    • N. Hyvönen, Application of a weaker formulation of the factorization method to the characterization of absorbing inclusions in optical tomography, Inverse Problems, 21 (2005), 1331– 1343.
    • (2005) Inverse Problems , vol.21 , pp. 1331-1343
    • Hyvönen, N.1
  • 18
    • 13744260991 scopus 로고    scopus 로고
    • A new formulation of the probe method and related problems
    • M. Ikehata, A new formulation of the probe method and related problems, Inverse Problems, 21 (2005), 413–426.
    • (2005) Inverse Problems , vol.21 , pp. 413-426
    • Ikehata, M.1
  • 20
    • 0000714376 scopus 로고    scopus 로고
    • Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
    • A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489–1512.
    • (1998) Inverse Problems , vol.14 , pp. 1489-1512
    • Kirsch, A.1
  • 21
    • 14544299658 scopus 로고    scopus 로고
    • The factorization method for a class of inverse elliptic problems
    • A. Kirsch, The factorization method for a class of inverse elliptic problems, Math. Nachr., 278 (2005), 258–277.
    • (2005) Math. Nachr. , vol.278 , pp. 258-277
    • Kirsch, A.1
  • 22
    • 33749018548 scopus 로고    scopus 로고
    • A regularization technique for the factorization method
    • A. Lechleiter, A regularization technique for the factorization method, Inverse Problems, 22, (2006), 1605–1625.
    • (2006) Inverse Problems , vol.22 , pp. 1605-1625
    • Lechleiter, A.1
  • 23
    • 0030550779 scopus 로고    scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71–96.
    • (1996) Ann. of Math. , vol.143 , pp. 71-96
    • Nachman, A.I.1
  • 24
    • 0000426306 scopus 로고
    • Reconstructions from boundary measurements
    • A. I. Nachman, Reconstructions from boundary measurements, Ann. of Math., 128 (1988), 531–576.
    • (1988) Ann. of Math. , vol.128 , pp. 531-576
    • Nachman, A.I.1
  • 26
    • 0037908702 scopus 로고    scopus 로고
    • Complex geometrical optics solutions for Lipschitz conductivities
    • L. Päivärinta, A. Panchenko and G. Uhlmann, Complex geometrical optics solutions for Lipschitz conductivities, Rev. Mat. Iberoamericana, 19 (2003), 57–72.
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 57-72
    • Päivärinta, L.1    Panchenko, A.2    Uhlmann, G.3
  • 27
    • 33748999350 scopus 로고    scopus 로고
    • A high-order finite element method for electrical impedance tomography
    • Proceedings, MA: The Electromagnetics Academy, Cambridge
    • S. Pursiainen and H. Hakula, A high-order finite element method for electrical impedance tomography, in “Progress in Electromagnetics Research Symposium 2006 Cambridge,” Proceedings vol 1, MA: The Electromagnetics Academy, Cambridge, p. 260.
    • Progress in Electromagnetics Research Symposium 2006 Cambridge , vol.1 , pp. 260
    • Pursiainen, S.1    Hakula, H.2
  • 28
    • 0000115945 scopus 로고    scopus 로고
    • An implementation of the reconstruction algorithm of A Nachman for the 2d inverse conductivity problem
    • S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A Nachman for the 2d inverse conductivity problem, Inverse Problems, 16 (2000), 681–699.
    • (2000) Inverse Problems , vol.16 , pp. 681-699
    • Siltanen, S.1    Mueller, J.2    Isaacson, D.3
  • 29
    • 0001606527 scopus 로고
    • Layer stripping: A direct numerical method for impedance imaging
    • E. Somersalo, M. Cheney, D. Isaacson D and E. Isaacson, Layer stripping: a direct numerical method for impedance imaging, Inverse Problems, 7 (1991), 899–926.
    • (1991) Inverse Problems , vol.7 , pp. 899-926
    • Somersalo, E.1    Cheney, M.2    Isaacson, D.3    Isaacson, E.4
  • 30
    • 0026907944 scopus 로고
    • Existence and uniqueness for electrode models for electric current computed tomography
    • E. Somersalo, M. Cheney and D. Isaacson, Existence and uniqueness for electrode models for electric current computed tomography, SIAM J. Appl. Math., 52 (1992), 1023–1040.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 1023-1040
    • Somersalo, E.1    Cheney, M.2    Isaacson, D.3
  • 31
    • 0000032419 scopus 로고
    • A convergent layer stripping algorithm for the radially symmetric impedance tomography problem
    • J. Sylvester, A convergent layer stripping algorithm for the radially symmetric impedance tomography problem, Comm. Partial Differential Equations, 17 (1992), 1955–1994.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 1955-1994
    • Sylvester, J.1
  • 32
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153–169.
    • (1987) Ann. of Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2


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