메뉴 건너뛰기




Volumn 67, Issue 3, 2007, Pages 893-913

D-bar method for electrical impedance tomography with discontinuous conductivities

Author keywords

Electrical impedance tomography; Exponentially growing solution; Faddeev's Green's function; Inverse conductivity problem

Indexed keywords

ELECTRICAL IMPEDANCE TOMOGRAPHY; EXPONENTIALLY GROWING SOLUTIONS; FADDEEV'S GREEN'S FUNCTION; INVERSE CONDUCTIVITY PROBLEM;

EID: 34547282631     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/060656930     Document Type: Article
Times cited : (80)

References (39)
  • 2
    • 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), pp. 265-299.
    • (2006) Ann. of Math. (2) , vol.163 , pp. 265-299
    • ASTALA, K.1    PÄIVÄRINTA, L.2
  • 4
    • 0035402391 scopus 로고    scopus 로고
    • Stability of the inverse conductivity problem in the plane for less regular conductivities
    • J. A. BARCELÓ, T. BARCELÓ, AND A. RUIZ, Stability of the inverse conductivity problem in the plane for less regular conductivities, J. Differential Equations, 173 (2001), pp, 231-270.
    • (2001) J. Differential Equations , vol.173 , pp. 231-270
    • BARCELÓ, J.A.1    BARCELÓ, T.2    RUIZ, A.3
  • 5
    • 0036904346 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • L. BORCEA, Electrical impedance tomography, Inverse Problems, 18 (2002), pp. 99-136.
    • (2002) Inverse Problems , vol.18 , pp. 99-136
    • BORCEA, L.1
  • 6
    • 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), pp. 1009-1027.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 1009-1027
    • BROWN, R.M.1    UHLMANN, G.2
  • 8
    • 0002621641 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • M. CHENEY, D. ISAACSON, AND J. C. NEWELL, Electrical impedance tomography, SIAM Rev., 41 (1999), pp. 85-101.
    • (1999) SIAM Rev , vol.41 , pp. 85-101
    • CHENEY, M.1    ISAACSON, D.2    NEWELL, J.C.3
  • 9
    • 0034036998 scopus 로고    scopus 로고
    • Electrical imaging of engineered hydraulic barriers
    • W. DAILY AND A. L. RAMIREZ, Electrical imaging of engineered hydraulic barriers, Geophysics, 65 (2000), pp. 83-94.
    • (2000) Geophysics , vol.65 , pp. 83-94
    • DAILY, W.1    RAMIREZ, A.L.2
  • 10
    • 0000724091 scopus 로고    scopus 로고
    • Electrical impedance tomography of a perchloroethylene release
    • W. DAILY, A. RAMIREZ, AND R. JOHNSON, Electrical impedance tomography of a perchloroethylene release, J. Environ. Eng. Geophys., 2 (1998), pp. 189-201.
    • (1998) J. Environ. Eng. Geophys , vol.2 , pp. 189-201
    • DAILY, W.1    RAMIREZ, A.2    JOHNSON, R.3
  • 11
    • 0012073739 scopus 로고
    • The application of electric current computed tomography to defect imaging in metals
    • Plenum Press, New York
    • M. R. EGGLESTON, R. J. SCHWABE, D. ISAACSON, AND L. F. COFFIN, The application of electric current computed tomography to defect imaging in metals, in Review of Progress in Quantitative NDE, Vol. 9A, Plenum Press, New York, 1990, pp. 455-462.
    • (1990) Review of Progress in Quantitative NDE , vol.9 A , pp. 455-462
    • EGGLESTON, M.R.1    SCHWABE, R.J.2    ISAACSON, D.3    COFFIN, L.F.4
  • 12
    • 0025545124 scopus 로고
    • Electric current computed tomography and eigenvalues
    • D. G. GISSER, D. ISAACSON, AND J. C. NEWELL, Electric current computed tomography and eigenvalues, SIAM J. Appl. Math., 50 (1990), pp. 1623-1634.
    • (1990) SIAM J. Appl. Math , vol.50 , pp. 1623-1634
    • GISSER, D.G.1    ISAACSON, D.2    NEWELL, J.C.3
  • 13
    • 0026374796 scopus 로고
    • Effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms
    • D. ISAACSON AND M. CHENEY, Effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms, SIAM J. Appl. Math., 51 (1989), pp. 1705-1731.
    • (1989) SIAM J. Appl. Math , vol.51 , pp. 1705-1731
    • ISAACSON, D.1    CHENEY, M.2
  • 15
    • 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. Imaging, 23 (2004) pp. 821-828.
    • (2004) IEEE Trans. Med. Imaging , vol.23 , pp. 821-828
    • ISAACSON, D.1    MUELLER, J.L.2    NEWELL, J.C.3    SILTANEN, S.4
  • 16
    • 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, Physiol. Meas., 27 (2006), pp. S43-S50.
    • (2006) Physiol. Meas , vol.27
    • ISAACSON, D.1    MUELLER, J.L.2    NEWELL, J.C.3    SILTANEN, S.4
  • 17
    • 0034655435 scopus 로고    scopus 로고
    • Complex resistivity tomography for environmental applications
    • A. KEMNA, A. BINLEY, A. RAMIREZ, AND W. DAILY. Complex resistivity tomography for environmental applications, Chem. Eng. J., 77 (2000), pp. 11-18.
    • (2000) Chem. Eng. J , vol.77 , pp. 11-18
    • KEMNA, A.1    BINLEY, A.2    RAMIREZ, A.3    DAILY, W.4
  • 18
    • 1842644664 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark
    • K. KNUDSEN, On the Inverse Conductivity Problem, Ph.D. thesis, Department of Mathematical Sciences, Aalborg University, Aalborg, 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), pp. 391-401.
    • (2003) Physiol. Meas , vol.24 , pp. 391-401
    • KNUDSEN, K.1
  • 20
    • 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), pp. 361-381.
    • (2004) Comm. Partial Differential Equations , vol.29 , pp. 361-381
    • KNUDSEN, K.1    TAMASAN, A.2
  • 21
    • 2342566028 scopus 로고    scopus 로고
    • Numerical solution method for the D-bar equation in the plane
    • K. KNUDSEN, J. L. MUELLER, AND S. SILTANEN, Numerical solution method for the D-bar equation in the plane, J. Comput. Phys., 198 (2004), pp. 500-517.
    • (2004) J. Comput. Phys , vol.198 , pp. 500-517
    • KNUDSEN, K.1    MUELLER, J.L.2    SILTANEN, S.3
  • 24
    • 0037505387 scopus 로고    scopus 로고
    • Direct reconstructions of conductivities from boundary measurements
    • J. L. MUELLER AND S. SILTANEN, Direct reconstructions of conductivities from boundary measurements, SIAM J. Sci. Comput., 24 (2003), pp. 1232-1266.
    • (2003) SIAM J. Sci. Comput , vol.24 , pp. 1232-1266
    • MUELLER, J.L.1    SILTANEN, S.2
  • 25
    • 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), pp. 71-96.
    • (1996) Ann. of Math. (2) , vol.143 , pp. 71-96
    • NACHMAN, A.I.1
  • 26
    • 0011586715 scopus 로고
    • Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem
    • Department of Mathematics, University of Rochester, Rochester, NY
    • A. I. NACHMAN, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, Preprint Series 19, Department of Mathematics, University of Rochester, Rochester, NY, 1993.
    • (1993) Preprint Series , vol.19
    • NACHMAN, A.I.1
  • 27
    • 0035248460 scopus 로고    scopus 로고
    • Electrical imaging at the large block test-Yucca Mountain, Nevada
    • A. L. RAMIREZ AND W. DAILY, Electrical imaging at the large block test-Yucca Mountain, Nevada, J. Appl. Geophys., 46 (2001), pp. 85-100.
    • (2001) J. Appl. Geophys , vol.46 , pp. 85-100
    • RAMIREZ, A.L.1    DAILY, W.2
  • 28
    • 0037498807 scopus 로고
    • Methods of Modern Mathematical Physics
    • 2nd ed, Academic Press, New York
    • M. REED AND B. SIMON, Methods of Modern Mathematical Physics. I: Functional Analysis, 2nd ed., Academic Press, New York, 1980.
    • (1980) Functional Analysis
    • REED, M.1    SIMON, B.2
  • 29
    • 0000115945 scopus 로고    scopus 로고
    • An implementation of the reconstruction algorithm of A. Nachman for the 2-D inverse conductivity problem
    • S. SILTANEN, J. MUELLER, AND D. ISAACSON, An implementation of the reconstruction algorithm of A. Nachman for the 2-D inverse conductivity problem, Inverse Problems, 16 (2000), pp. 681-699.
    • (2000) Inverse Problems , vol.16 , pp. 681-699
    • SILTANEN, S.1    MUELLER, J.2    ISAACSON, D.3
  • 30
    • 0034077577 scopus 로고    scopus 로고
    • Cross-hole electrical imaging of a controlled saline tracer injection
    • L. SLATER, A. M. BINLEY, W. DAILY, AND R. JOHNSON, Cross-hole electrical imaging of a controlled saline tracer injection, J. Appl. Geophys., 44 (2000), pp. 85-102.
    • (2000) J. Appl. Geophys , vol.44 , pp. 85-102
    • SLATER, L.1    BINLEY, A.M.2    DAILY, W.3    JOHNSON, R.4
  • 31
    • 0001156477 scopus 로고
    • Sur la distribution électrique potentielle autour d'une prise de terre ponctuelle dans un terrain à couches horizontales, homogènes et isotropes, J
    • S. STEPANESCU, C. SCHLUMBERGER, AND M. SCHLUMBERGER, Sur la distribution électrique potentielle autour d'une prise de terre ponctuelle dans un terrain à couches horizontales, homogènes et isotropes, J. Physics and Radium Ser., 7 (1930), pp. 132-140.
    • (1930) Physics and Radium Ser , vol.7 , pp. 132-140
    • STEPANESCU, S.1    SCHLUMBERGER, C.2    SCHLUMBERGER, M.3
  • 32
    • 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), pp. 1955-1994.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 1955-1994
    • SYLVESTER, J.1
  • 34
    • 0347517837 scopus 로고    scopus 로고
    • Electrical impedance tomography using the extended Kalman filter
    • F. C. TRIGO, R. GONZALEZ-LIMA, AND M. B. P. AMATO, Electrical impedance tomography using the extended Kalman filter, IEEE Trans. Biomed. Eng., 51 (2004), pp. 72-81.
    • (2004) IEEE Trans. Biomed. Eng , vol.51 , pp. 72-81
    • TRIGO, F.C.1    GONZALEZ-LIMA, R.2    AMATO, M.B.P.3
  • 36
    • 34547311698 scopus 로고    scopus 로고
    • R. A. WILLIAMS AND M. S. BECK, EDS., Process Tomography-Principles, Techniques, and Applications, Butterworth-Heinemann, Oxford, UK, 1995.
    • R. A. WILLIAMS AND M. S. BECK, EDS., Process Tomography-Principles, Techniques, and Applications, Butterworth-Heinemann, Oxford, UK, 1995.
  • 37
    • 5244307092 scopus 로고
    • Tomographic imaging of industrial process equipment-development of system model and image reconstruction algorithm for capacitive tomography
    • Edinburgh, Scotland
    • C. G. XIE, S. M. HUANG, B. S. HOYLE, AND M. S. BECK, Tomographic imaging of industrial process equipment-development of system model and image reconstruction algorithm for capacitive tomography, in Proceedings of the 5th Conference on Sensors and Their Applications, Edinburgh, Scotland, 1991, pp. 203-208.
    • (1991) Proceedings of the 5th Conference on Sensors and Their Applications , pp. 203-208
    • XIE, C.G.1    HUANG, S.M.2    HOYLE, B.S.3    BECK, M.S.4
  • 38
    • 0000627554 scopus 로고    scopus 로고
    • Developments in inverse problems since Calderun's foundational paper
    • Chicago, IL, University of Chicago Press, Chicago, IL
    • G. A. UHLMANN, Developments in inverse problems since Calderun's foundational paper, in Harmonic Analysis and Partial Differential Equations (Chicago, IL, 1996), University of Chicago Press, Chicago, IL, 1999.
    • (1996) Harmonic Analysis and Partial Differential Equations
    • UHLMANN, G.A.1
  • 39
    • 34347233191 scopus 로고
    • 8-electrode capacitance system for two-component flow identification
    • C. G. XIE, A. PLASKOWSKI, AND M. S. BECK, 8-electrode capacitance system for two-component flow identification, IEEE Proc. A, 136 (1989), pp. 173-190.
    • (1989) IEEE Proc. A , vol.136 , pp. 173-190
    • XIE, C.G.1    PLASKOWSKI, A.2    BECK, M.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.