메뉴 건너뛰기




Volumn 5, Issue 3, 2011, Pages 531-549

Direct electrical impedance tomography for nonsmooth conductivities

Author keywords

Beltrami equation; Complex geometrical optics solution; Conductivity equation; Electrical impedance tomography; Inverse conductivity problem; Inverse problem; Nonlinear Fourier transform; Numerical solver; Quasiconformal map

Indexed keywords


EID: 80051907624     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2011.5.531     Document Type: Article
Times cited : (23)

References (34)
  • 1
    • 30444450433 scopus 로고    scopus 로고
    • Calderón's inverse conductivity problem in the plane
    • K. Astala and L. Päivärinta, Calderón's inverse conductivity problem in the plane, Ann. of Math. (2), 163 (2006), 265-299.
    • (2006) Ann. of Math , vol.163 , Issue.2 , pp. 265-299
    • Astala, K.1    Päivärinta, L.2
  • 2
  • 4
    • 84883906715 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane
    • Princeton University Press, Princeton, NJ
    • K. Astala, T. Iwaniec and G. Martin, "Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, " Princeton Mathematical Series, 48, Princeton University Press, Princeton, NJ, 2009.
    • (2009) Princeton Mathematical Series , vol.48
    • Astala, K.1    Iwaniec, T.2    Martin, G.3
  • 5
  • 6
    • 78651379669 scopus 로고    scopus 로고
    • Direct numerical reconstruction of conductivities in three dimensions using scattering transforms
    • J. Bikowski, K. Knudsen and J. L. Mueller, Direct numerical reconstruction of conductivities in three dimensions using scattering transforms, Inverse Problems, 27 (2011), 19 pp.
    • (2011) Inverse Problems , vol.27 , pp. 19
    • Bikowski, J.1    Knudsen, K.2    Mueller, J.L.3
  • 8
    • 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
  • 10
  • 12
    • 0042582033 scopus 로고
    • A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings
    • P. Daripa, A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings, Journal of Computational Physics, 106 (1993), 355-365.
    • (1993) Journal of Computational Physics , vol.106 , pp. 355-365
    • Daripa, P.1
  • 13
    • 75449106051 scopus 로고    scopus 로고
    • D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform
    • M. DeAngelo and J. L. Mueller, D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform, Physiological Measurement, 31 (2010), 221-232.
    • (2010) Physiological Measurement , vol.31 , pp. 221-232
    • DeAngelo, M.1    Mueller, J.L.2
  • 16
    • 3142723330 scopus 로고    scopus 로고
    • Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography
    • D. Isaacson, J. L. Mueller, J. C. Newell and S. Siltanen, Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography, IEEE Trans. Med. Im., 23 (2004), 821-828.
    • (2004) IEEE Trans. Med. Im , vol.23 , pp. 821-828
    • Isaacson, D.1    Mueller, J.L.2    Newell, J.C.3    Siltanen, S.4
  • 17
    • 33745160014 scopus 로고    scopus 로고
    • Imaging cardiac activity by the D-bar method for electrical impedance tomography
    • D. Isaacson, J. L. Mueller, J. C. Newell and S. Siltanen, Imaging cardiac activity by the D-bar method for electrical impedance tomography, Physiological Measurement, 27 (2006), S43-S50.
    • (2006) Physiological Measurement , vol.27
    • Isaacson, D.1    Mueller, J.L.2    Newell, J.C.3    Siltanen, S.4
  • 18
    • 1842644664 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Mathematical Sciences, Aalborg University, Denmark
    • K. Knudsen, "On the Inverse Conductivity Problem, " Ph.D. thesis, Department of Mathematical Sciences, Aalborg University, Denmark, 2002.
    • (2002) On the Inverse Conductivity Problem
    • Knudsen, K.1
  • 19
    • 0038777528 scopus 로고    scopus 로고
    • A new direct method for reconstructing isotropic conductivities in the plane
    • K. Knudsen, A new direct method for reconstructing isotropic conductivities in the plane, Physiol. Meas., 24 (2003), 391-401.
    • (2003) Physiol. Meas , vol.24 , pp. 391-401
    • Knudsen, K.1
  • 21
    • 34547282631 scopus 로고    scopus 로고
    • D-bar method for electrical impedance tomography with discontinuous conductivities
    • K. Knudsen, M. Lassas, J. L. Mueller and S. Siltanen, D-bar method for electrical impedance tomography with discontinuous conductivities, SIAM J. Appl. Math., 67 (2007), 893-913.
    • (2007) SIAM J. Appl. Math , vol.67 , pp. 893-913
    • Knudsen, K.1    Lassas, M.2    Mueller, J.L.3    Siltanen, S.4
  • 23
    • 2342566028 scopus 로고    scopus 로고
    • Numerical solution method for the dbar-equation in the plane
    • K. Knudsen, J. L. Mueller and S. Siltanen, Numerical solution method for the dbar-equation in the plane, J. Comp. Phys., 198 (2004), 500-517.
    • (2004) J. Comp. Phys , vol.198 , pp. 500-517
    • Knudsen, K.1    Mueller, J.L.2    Siltanen, S.3
  • 24
    • 1842683121 scopus 로고    scopus 로고
    • Reconstruction of less regular conductivities in the plane
    • K. Knudsen and A. Tamasan, Reconstruction of less regular conductivities in the plane, Comm. Partial Differential Equations, 29 (2004), 361-381.
    • (2004) Comm. Partial Differential Equations , vol.29 , pp. 361-381
    • Knudsen, K.1    Tamasan, A.2
  • 25
    • 0037505387 scopus 로고    scopus 로고
    • Direct reconstructions of conductivities from boundary mea-surements
    • J. L. Mueller and S. Siltanen, Direct reconstructions of conductivities from boundary mea-surements, SIAM J. Sci. Comp., 24 (2003), 1232-1266.
    • (2003) SIAM J. Sci. Comp , vol.24 , pp. 1232-1266
    • Mueller, J.L.1    Siltanen, S.2
  • 26
    • 0036591472 scopus 로고    scopus 로고
    • A direct reconstruction algorithm for electrical impedance tomography
    • J. L. Mueller, S. Siltanen and D. Isaacson, A direct reconstruction algorithm for electrical impedance tomography, IEEE Trans. Med. Im., 21 (2002), 555-559.
    • (2002) IEEE Trans. Med. Im , vol.21 , pp. 555-559
    • Mueller, J.L.1    Siltanen, S.2    Isaacson, D.3
  • 27
    • 34447107059 scopus 로고    scopus 로고
    • Reconstruction of conductive and insulating targets using the D-bar method on an elliptical domain
    • E. Murphy, J. L. Mueller and J. C. Newell, Reconstruction of conductive and insulating targets using the D-bar method on an elliptical domain, Physiol. Meas., 28 (2007), S101-S114.
    • (2007) Physiol. Meas , vol.28
    • Murphy, E.1    Mueller, J.L.2    Newell, J.C.3
  • 28
    • 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. (2), 143 (1996), 71-96.
    • (1996) Ann. of Math , vol.143 , Issue.2 , pp. 71-96
    • Nachman, A.I.1
  • 29
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), 856-869.
    • (1986) SIAM J. Sci. Stat. Comput , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 30
    • 0000115945 scopus 로고    scopus 로고
    • An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem
    • (Erratum: Inverse problems, 17, 1561-1563)
    • 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, (Erratum: Inverse problems, 17, 1561-1563).
    • (2000) Inverse Problems , vol.16 , pp. 681-699
    • Siltanen, S.1    Mueller, J.2    Isaacson, D.3
  • 31
    • 0038519398 scopus 로고    scopus 로고
    • Reconstruction of High Contrast 2-D Conductivities by the Algorithm of A. Nachman
    • In, (South Hadley, MA), Contemporary Mathematics, 278, Amer. Math. Soc., Providence, RI, 2001
    • S. Siltanen, J. Mueller and D. Isaacson, "Reconstruction of High Contrast 2-D Conductivities by the Algorithm of A. Nachman, " In "Radon Transforms and Tomography" (South Hadley, MA, 2000), 241-254, Contemporary Mathematics, 278, Amer. Math. Soc., Providence, RI, 2001.
    • (2000) Radon Transforms and Tomography , pp. 241-254
    • Siltanen, S.1    Mueller, J.2    Isaacson, D.3
  • 34
    • 0037842986 scopus 로고    scopus 로고
    • Fast solvers of the Lippmann-Schwinger equation
    • in, (Newark, DE), Int. Soc. Anal. Appl. Comput., Kluwer Acad. Publ, Dordrecht, 2000
    • G. Vainikko, Fast solvers of the Lippmann-Schwinger equation, in "Direct and Inverse Problems of Mathematical Physics" (Newark, DE, 1997), 423-440, Int. Soc. Anal. Appl. Comput., 5, Kluwer Acad. Publ, Dordrecht, 2000.
    • (1997) Direct and Inverse Problems of Mathematical Physics , vol.5 , pp. 423-440
    • Vainikko, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.