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Volumn 27, Issue 1, 2011, Pages

Direct numerical reconstruction of conductivities in three dimensions using scattering transforms

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX GEOMETRICAL OPTICS; CONDUCTIVITY DISTRIBUTIONS; FORWARD PROBLEM; LINEAR RECONSTRUCTION; NONLINEAR SCATTERING; NUMERICAL RECONSTRUCTION; RECONSTRUCTION ALGORITHMS; SCATTERING TRANSFORMS; TEST PROBLEM; THREE DIMENSIONS;

EID: 78651379669     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/27/1/015002     Document Type: Article
Times cited : (43)

References (37)
  • 1
    • 36348940659 scopus 로고    scopus 로고
    • A boundary integral equation for Calderón's inverse conductivity problem
    • [AP06a]
    • [AP06a] Astala K and Päivärinta L 2006 A boundary integral equation for Calderón's inverse conductivity problem Collect. Math. 127-39
    • (2006) Collect. Math. , pp. 127-39
    • Astala, K.1    Päivärinta, L.2
  • 2
    • 30444450433 scopus 로고    scopus 로고
    • Calderón's inverse conductivity problem in the plane
    • [AP06b]
    • [AP06b] Astala K and Päivärinta L 2006 Calderón's inverse conductivity problem in the plane Ann. Math. 163 265-99
    • (2006) Ann. Math. , vol.163 , pp. 265-299
    • Astala, K.1    Päivärinta, L.2
  • 3
    • 67649545051 scopus 로고    scopus 로고
    • 2D EIT reconstructions using Calderón's method
    • [BM08]
    • [BM08] Bikowski J and Mueller J 2008 2D EIT reconstructions using Calderón's method Inverse Problem Imaging 2 43-61
    • (2008) Inverse Problem Imaging , vol.2 , pp. 43-61
    • Bikowski, J.1    Mueller, J.2
  • 6
    • 0001659228 scopus 로고    scopus 로고
    • Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
    • [BU97]
    • [BU97] Brown R and Uhlmann G 1997 Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions Commun. Partial Differ. Eqns 22 1009-27
    • (1997) Commun. Partial Differ. Eqns , vol.22 , pp. 1009-27
    • Brown, R.1    Uhlmann, G.2
  • 7
    • 0002713385 scopus 로고
    • On an inverse boundary value problem
    • [Cal80], (Rio de Janeiro, 1980) (Rio de Janeiro: Brazilian Mathematical Society)
    • [Cal80] Calderón A 1980 On an inverse boundary value problem Seminar on Numerical Analysis and Its Applications to Continuum Physics (Rio de Janeiro, 1980) (Rio de Janeiro: Brazilian Mathematical Society) pp 65-73
    • (1980) Seminar on Numerical Analysis and Its Applications to Continuum Physics , pp. 65-73
    • Calderón, A.1
  • 8
    • 33746091726 scopus 로고    scopus 로고
    • Towards a d-bar reconstructionmethod for three-dimensional EIT
    • [CKS06]
    • [CKS06] Cornean H, KnudsenKand Siltanen S 2006 Towards a d-bar reconstructionmethod for three-dimensional EIT J. Inverse Ill-Posed Problem 14 111-34
    • (2006) J. Inverse Ill-Posed Problem , vol.14 , pp. 111-134
    • Cornean, H.1    Knudsen, K.2    Siltanen, S.3
  • 9
    • 75449106051 scopus 로고    scopus 로고
    • D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform
    • [DM10]
    • [DM10] DeAngeloMand Mueller J 2010 D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform Physiol. Meas. 31 221-32
    • (2010) Physiol. Meas. , vol.31 , pp. 221-32
    • De Angelo Mand Mueller, J.1
  • 10
    • 0035661810 scopus 로고    scopus 로고
    • On a numerical solution of a three-dimensional inverse medium scattering problem
    • [Hoh01]
    • [Hoh01] Hohage T 2001 On a numerical solution of a three-dimensional inverse medium scattering problem Inverse Problems 17 1743-63
    • (2001) Inverse Problems , vol.17 , pp. 1743-1763
    • Hohage, T.1
  • 12
    • 22544453369 scopus 로고    scopus 로고
    • [Hol05], 1st edn (Bristol: Institute of Physics Publishing)
    • [Hol05] Holder D 2005 Electrical Impedance Tomography 1st edn (Bristol: Institute of Physics Publishing)
    • (2005) Electrical Impedance Tomography
    • Holder, D.1
  • 13
    • 3142723330 scopus 로고    scopus 로고
    • Reconstructions of chest phatoms by the D-bar method for electrical impedance tomography
    • [IMNS04]
    • [IMNS04] Isaacson D, Mueller J, Newell J and Siltanen S 2004 Reconstructions of chest phatoms by the D-bar method for electrical impedance tomography IEEE Trans. Med. Imaging 23 821-8
    • (2004) IEEE Trans. Med. Imaging , vol.23 , pp. 821-828
    • Isaacson, D.1    Mueller, J.2    Newell, J.3    Siltanen, S.4
  • 14
    • 33745160014 scopus 로고    scopus 로고
    • Imaging cardiac activity by the D-bar method for electrical impedance tomography
    • [IMNS06]
    • [IMNS06] Isaacson D, Mueller J, Newell J and Siltanen S 2006 Imaging cardiac activity by the D-bar method for electrical impedance tomography Physiol. Meas. 27 S43-50
    • (2006) Physiol. Meas. , vol.27
    • Isaacson, D.1    Mueller, J.2    Newell, J.3    Siltanen, S.4
  • 15
    • 0038777528 scopus 로고    scopus 로고
    • A new direct method for reconstructing isotropic conductivities in the plane
    • [Knu03]
    • [Knu03] Knudsen K 2003 A new direct method for reconstructing isotropic conductivities in the plane Physiol. Meas. 24 391-401
    • (2003) Physiol. Meas. , vol.24 , pp. 391-401
    • Knudsen, K.1
  • 16
    • 34547282631 scopus 로고    scopus 로고
    • D-barmethod for electrical impedance tomography with discontinuous conductivities
    • [KLMS07]
    • [KLMS07] Knudsen K, LassasM,Mueller J and Siltanen S 2007 D-barmethod for electrical impedance tomography with discontinuous conductivities SIAM J. Appl. Math. 67 893-913
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 893-913
    • Knudsen, K.1    Lassas, M.2    Mueller, J.3    Siltanen, S.4
  • 17
    • 73649113504 scopus 로고    scopus 로고
    • Regularized D-bar method for the inverse conductivity problem
    • [KLMS09]
    • [KLMS09] Knudsen K, Lassas M, Mueller J and Siltanen S 2009 Regularized D-bar method for the inverse conductivity problem Inverse Problem Imaging 3 599-624
    • (2009) Inverse Problem Imaging , vol.3 , pp. 599-624
    • Knudsen, K.1    Lassas, M.2    Mueller, J.3    Siltanen, S.4
  • 18
    • 2342566028 scopus 로고    scopus 로고
    • Numerical solution method of the D-bar-equation in the plane
    • [KMS04]
    • [KMS04] Knudsen K, Mueller J and Siltanen S 2004 Numerical solution method of the D-bar-equation in the plane J. Comput. Phys. 198 500-17
    • (2004) J. Comput. Phys. , vol.198 , pp. 500-517
    • Knudsen, K.1    Mueller, J.2    Siltanen, S.3
  • 19
    • 1842683121 scopus 로고    scopus 로고
    • Reconstruction of less regular conductivities in the plane
    • [KT04]
    • [KT04] Knudsen K and Tamasan A 2004 Reconstruction of less regular conductivities in the plane Commun. Partial Differ. Eqns 29 361-81
    • (2004) Commun. Partial Differ. Eqns , vol.29 , pp. 361-381
    • Knudsen, K.1    Tamasan, A.2
  • 20
    • 0037505387 scopus 로고    scopus 로고
    • Direct reconstruction of conductivities from boundary measurements
    • [MS03]
    • [MS03] Mueller J and Siltanen S 2003 Direct reconstruction of conductivities from boundary measurements SIAM J. Sci. Comput. 24 1232-66
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1232-1266
    • Mueller, J.1    Siltanen, S.2
  • 21
    • 70349884116 scopus 로고    scopus 로고
    • Effect of errors in domain shape modeling in 2-d reconstructions by the D-bar method
    • [EM09]
    • [EM09] Murphy E and Mueller J 2009 Effect of errors in domain shape modeling in 2-d reconstructions by the D-bar method IEEE Trans. Med. Imaging 28 1576-84
    • (2009) IEEE Trans. Med. Imaging , vol.28 , pp. 1576-84
    • Murphy, E.1    Mueller, J.2
  • 22
    • 0000426306 scopus 로고
    • Reconstructions from boundary measurements
    • [Nac88]
    • [Nac88] Nachman A 1988 Reconstructions from boundary measurements Ann. Math. 128 531-76
    • (1988) Ann. Math. , vol.128 , pp. 531-576
    • Nachman, A.1
  • 23
    • 0030550779 scopus 로고    scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • [Nac96]
    • [Nac96] Nachman A 1996 Global uniqueness for a two-dimensional inverse boundary value problem Ann. Math. 143 71-96
    • (1996) Ann. Math. , vol.143 , pp. 71-96
    • Nachman, A.1
  • 25
    • 0001875067 scopus 로고
    • A multidimensional inverse spectral problem for the equation ΔΨ + (v(x) - Eu(x))Ψ = 0
    • [Nov88], 96
    • [Nov88] Novikov R 1988 A multidimensional inverse spectral problem for the equation ΔΨ + (v(x) - Eu(x))Ψ = 0 Funktsional Anal. i Prilozhen. 22 11-22, 96
    • (1988) Funktsional Anal. I Prilozhen. , vol.22 , pp. 11-22
    • Novikov, R.1
  • 28
    • 78651364167 scopus 로고    scopus 로고
    • Recovering conductivity at the boundary in three-dimensional electrical impedance tomography
    • [NRST10], to appear
    • [NRST10] Nakamura G, Ronkanen P, Siltanen S and Tanuma K 2010 Recovering conductivity at the boundary in three-dimensional electrical impedance tomography Inverse Problem Imaging to appear
    • (2010) Inverse Problem Imaging
    • Nakamura, G.1    Ronkanen, P.2    Siltanen, S.3    Tanuma, K.4
  • 29
    • 0037908702 scopus 로고    scopus 로고
    • Complex geometrical optics solutions for Lipschitz conductivities
    • [PPU03]
    • [PPU03] Päivärinta L, Panchenko A and Uhlmann G 2003 Complex geometrical optics solutions for Lipschitz conductivities Rev. Mat. Iberoamericana 19 56-72
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 56-72
    • Päivärinta, L.1    Panchenko, A.2    Uhlmann, G.3
  • 30
    • 0001606527 scopus 로고
    • Layer stripping: A direct numerical method for impedance imaging
    • [SCII91]
    • [SCII91] Somersalo E, Cheney M, Isaacson D and Isaacson E 1991 Layer stripping: a direct numerical method for impedance imaging Inverse Problems 7 899-926
    • (1991) Inverse Problems , vol.7 , pp. 899-926
    • Somersalo, E.1    Cheney, M.2    Isaacson, D.3    Isaacson, E.4
  • 31
    • 0000115945 scopus 로고    scopus 로고
    • An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem
    • [SMI00], (erratum)
    • [SMI00] Siltanen S, Mueller J and Isaacson D 2000 An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem Inverse Problems 16 681-99
    • Inverse Problems , vol.16 , pp. 681-699
    • Siltanen, S.1    Mueller, J.2    Isaacson, D.3
  • 33
    • 0038519398 scopus 로고    scopus 로고
    • Reconstruction of high contrast 2-D conductivities by the algorithm of A. Nachman
    • [SMI01], (South Hadley, MA, 2000) (Contemp. Math. ) (Providence, RI: American Mathematical Society)
    • [SMI01] Siltanen S, Mueller J and Isaacson D 2001 Reconstruction of high contrast 2-D conductivities by the algorithm of A. Nachman Radon Transforms and Tomography (South Hadley, MA, 2000) (Contemp. Math. vol 278) (Providence, RI: American Mathematical Society) pp 241-54
    • (2001) Radon Transforms and Tomography , vol.278 , pp. 241-254
    • Siltanen, S.1    Mueller, J.2    Isaacson, D.3
  • 35
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • [SS86]
    • [SS86] SaadYand SchultzM1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 7 856-69
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.2
  • 36
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • [SU87]
    • [SU87] Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem Ann. Math. 125 153-69
    • (1987) Ann. Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 37
    • 0037842986 scopus 로고    scopus 로고
    • Fast solvers of the Lippmann-Schwinger equation
    • [Vai00], (Newark, DE, 1997) (Dordrecht: Kluwer)
    • [Vai00] Vainikko G 2000 Fast solvers of the Lippmann-Schwinger equation Direct and Inverse Problems of Mathematical Physics (Newark, DE, 1997) (Dordrecht: Kluwer) pp 423-40
    • (2000) Direct and Inverse Problems of Mathematical Physics , pp. 423-440
    • Vainikko, G.1


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