A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D

Inverse Problems

Volumn 28, Issue 9, 2012, Pages

  Hamilton, S J ^a   Herrera, C N L ^b   Mueller, J L ^a   Von Herrmann, A ^c  

^a Veterinary Dentistry and Oral Surgery   (United States)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c DEPAUW UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEST PHANTOM; COMPLEX CONDUCTIVITY; D-BAR METHOD; DIRICHLET-TO-NEUMANN; EXPONENTIALLY GROWING SOLUTION; LIPSCHITZ DOMAIN; RECONSTRUCTION ALGORITHMS; SCATTERING TRANSFORMS; TWO-DIMENSION;

INVERSE PROBLEMS;

ALGORITHMS;

EID: 84866328113     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/28/9/095005     Document Type: Article

References (49)

1. Astala K and Päivärinta L 2006 Calderóns inverse conductivity problem in the plane Ann. Math. 163 265-99 (Pubitemid 44077802)
2. Astala K, Lassas M and Päivärinta L 2005 Calderóns inverse problem for anisotropic conductivity in the plane Commun. Partial Differ. Eqns 30 207-24 (Pubitemid 40549852)
3. Astala K, Mueller J L, Päivärinta L and Siltanen S 2010 Numerical computation of complex geometrical optics solutions to the conductivity equation Appl. Comput. Harmon. Anal. 29 2-17
4. Astala K, Mueller J L, Päivärinta L, Perämäki A and Siltanen S 2011 Direct electrical impedance tomography for nonsmooth conductivities Inverse Problems Imaging 5 531-50
5. Barceló J A, Barceló T and Ruiz A 2001 Stability of the inverse conductivity problem in the plane for less regular conductivities J. Differ. Eqns 173 231-70 (Pubitemid 33377548)
6. Bikowski J and Mueller J L 2008 2D EIT reconstructions using Calderóns method Inverse Problems Imaging 2 43-61
7. Boverman G, Kao T-J, Kulkarni R, Kim B S, Isaacson D, Saulnier G J and Newell J C 2008 Robust linearized image reconstruction for multifrequency EIT of the breast IEEE Trans. Med. Eng. 27 1439-48
8. Brown B H, Barber D C, Morice A H, Leathard A and Sinton A 1994 Cardiac and respiratory related electrical impedance changes in the human thorax IEEE Trans. Biomed. Eng. 41 729-34 (Pubitemid 24273256)
9. Brown R M and Uhlmann G 1997 Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions Commun. Partial Differ. Eqns 22 1009-27 (Pubitemid 127361562)
10. Bukhgeim A L 2007 Recovering a potential from cauchy data in the two-dimensional case Inverse Problems 15 1-15
11. Calderón A P 1980 On an inverse boundary value problem Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro: Sociedade Brasileira de Matemàtica) pp 65-73
12. Cheney M, Isaacson D and Newell J C 1999 Electrical impedance tomography SIAM Rev. 41 85-101 (Pubitemid 129723749)
13. Cheng K-S, Isaacson D, Newell J C and Gisser D G 1989 Electrode models for electric current computed tomography IEEE Trans. Biomed. Eng. 36 918-24 (Pubitemid 19232669)
14. Cook R D, Saulnier G J and Goble J C 1991 A phase sensitive voltmeter for a high-speed, high precision electrical impedance tomograph Proc. Annu. Int. Conf. IEEE Engineering in Medicine and Biology Society 30 22-3
15. Costa E L V, Chaves C N, Gomes S, Gonzalez Lima R and Amato M B P 2008 Real-time detection of pneumothorax using electrical impedance tomography Crit. Care Med. 36 1230-8 (Pubitemid 351482673)
16. Costa E L V, Gonzalez Lima R and Amato M B P 2009 Electrical impedance tomography Curr. Opin. Crit. Care 15 18-24
17. DeAngelo M and Mueller J L 2010 D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform Physiol. Meas. 31 221-32
18. Edic P M, Isaacson D, Saulnier G J, Jain H and Newell J C 1998 An iterative Newton-Raphson method to solve the inverse admittivity problem IEEE Trans. Biomed. Eng. 45 899-908 (Pubitemid 28292328)
19. Faddeev L D 1966 Increasing solutions of the Schrödinger equation Sov. Phys. Dokl. 10 1033-5
20. Francini E 2000 Recovering a complex coefficient in a planar domain from the Dirichlet-to-Neumann map Inverse Problems 6 107-19
21. Frerichs I, Hinz J, Herrmann P, Weisser G, Hahn G, Dudykevych T, Quintel M and Hellige G 2002 Detection of local lung air content by electrical impedance tomography compared with electron beam CT J. Appl. Physiol. 93 660-6 (Pubitemid 34810231)
22. Frerichs I, Hinz J, Herrmann P, Weisser G, Hahn G, Quintel M and Hellige G 2002 Regional lung perfusion as determined by electrical impedance tomography in comparison with electron beam CT imaging IEEE Trans. Med. Imaging 21 646-52 (Pubitemid 34950083)
23. Frerichs I, Schmitz G, Pulletz S, Schädler D, Zick G, Scholz J and Weiler N 2007 Reproducibility of regional lung ventilation distribution determined by electrical impedance tomography during mechanical ventilation Physiol. Meas. 28 261-7
24. Fuks L F, Cheney M, Isaacson D, Gisser D G and Newell J C 1991 Detection and imaging of electric conductivity and permittivity at low frequency IEEE Trans. Biomed. Eng. 38 1106-10
25. 2, ∞(Ω) for the 2D EIT problem PhD Thesis Colorado State University
26. Mueller J L, Siltanen S and Isaacson D 2003 A direct reconstruction algorithm for electrical impedance tomography IEEE Trans. Med. Imaging 21 555-9
27. Isaacson D, Mueller J L, Newell J C and Siltanen S 2004 Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography IEEE Trans. Med. Imaging 23 821-8
28. Isaacson D, Mueller J L, Newell J C and Siltanen S 2006 Imaging cardiac activity by the D-bar method for electrical impedance tomography Physiol. Meas. 27 S43-50 (Pubitemid 43890632)
29. Jain H, Isaacson D, Edic P M and Newell J C 1997 Electrical impedance tomography of complex conductivity distributions with noncircular boundary IEEE Trans. Biomed. Eng. 44 1051-60 (Pubitemid 27467383)
30. Kao T-J, Boverman G, Kim S B, Isaacson D, Saulnier G J, Newell J C, Choi M H, Moore R H and Kopans D B 2008 Regional admittivity spectra with tomosynthesis images for breast cancer detection: preliminary patient study IEEE Trans. Med. Imaging 27 1762-8
31. Kerner T E, Paulsen K D, Hartov A, Soho S K and Poplack S P 2002 Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects IEEE Trans. Med. Imaging 21 638-45 (Pubitemid 34950082)
32. Knudsen K 2002 On the inverse conductivity problem PhD Thesis Department of Mathematical Sciences, Aalborg University, Denmark
33. Knudsen K 2003 A new direct method for reconstructing isotropic conductivities in the plane Physiol. Meas. 24 391-401 (Pubitemid 36648405)
34. Knudsen K and Tamasan A 2004 Reconstruction of less regular conductivities in the plane Commun. Partial Differ. Eqns 29 361-81 (Pubitemid 38482891)
35. Knudsen K, Mueller J L and Siltanen S 2004 Numerical solution method for the Dbar-equation in the plane J. Comput. Phys. 198 500-17 (Pubitemid 38999049)
36. Vainikko G 2000 Fast solvers of the Lippmann-Schwinger equation Direct and Inverse Problems of Mathematical Physics (International Society for Analysis, Applications and Computation vol 5) (Dordrecht: Kluwer) pp 423-40
37. Knudsen K, Lassas M, Mueller J L and Siltanen S 2008 Reconstructions of piecewise constant conductivities by the D-bar method for electrical impedance tomography Proc. 4th AIP Int. Conf. and the 1st Congr. IPIA (Vancouver,) 012029
38. Knudsen K, Lassas M, Mueller J L and Siltanen S 2007 D-bar method for electrical impedance tomography with discontinuous conductivities SIAM J. Appl. Math. 67 893-913 (Pubitemid 47138335)
39. Knudsen K, Lassas M, Mueller J L and Siltanen S 2009 Regularized D-bar method for the inverse conductivity problem Inverse Problems Imaging 3 599-624
40. Mueller J L and Siltanen S 2003 Direct reconstructions of conductivities from boundary measurements SIAM J. Sci. Comput. 24 1232-66
41. Murphy E, Mueller J L and Newell J C 2007 Reconstruction of conductive and insulating targets using the D-bar method on an elliptical domain Physiol. Meas. 28 S101-14 (Pubitemid 47028475)
42. Nachman A I 1996 Global uniqueness for a two-dimensional inverse boundary value problem Ann. Math. 143 71-96
43. 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
44. Siltanen S 1999 Electrical impedance tomography and Faddeev Greens functions PhD Thesis Helsinki University of Technology Espoo, Finland
45. Smit H, Vonk Noordegraaf A, Marcus J T, Boonstra A, de Vries P M and Postmus P E 2004 Determinants of pulmonary perfusion measured by electrical impedance tomography Eur. J. Appl. Physiol. 92 45-9 (Pubitemid 38885859)
46. Tidswell A T, Gibson A, Bayford R H and Holder D S 2001 Three-dimensional electrical impedance tomography of human brain activity Neuroimage 13 283-94 (Pubitemid 34185017)
47. Tidswell A T, Gibson A, Bayford R H and Holder D S 2001 Validation of a 3D reconstruction algorithm for EIT of human brain function in a realistic head-shaped tank Physiol. Meas. 22 177-85 (Pubitemid 32186770)
48. Victorino J A et al 2004 Imbalances in regional lung ventilation: a validation study on electrical impedance tomography Am. J. Respir. Crit. Care Med. 169 791-800 (Pubitemid 38402453)
49. 1, p(Ω) in the plane PhD Thesis Colorado State University