High-contrast impedance tomography

Inverse Problems

Volumn 12, Issue 6, 1996, Pages 835-858

  Borcea, Liliana ^a   Berryman, James G ^b   Papanicolaou, George C ^a  

^a STANFORD UNIVERSITY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001658166     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/12/6/003     Document Type: Article

References (47)

1. Allen A and Santosa F 1991 Stability and resolution analysis of a linearized problem in electrical impedance tomography Inverse Problems 7 515-33
2. Alessandrini G 1988 Stable determination of conductivity by boundary measurements Appl. Anal. 27 153-72
3. Alumbaugh D L and Morrison H F 1993 Electromagnetic conductivity imaging with an iterative Born inversion IEEE Trans. Geosci. Remote Sensing 31 758-63
4. Alumbaugh D L and Morrison H F 1995 Monitoring subsurface changes over time with cross-well electromagnetic tomography Geophys. Prospecting 43 873-902
5. Bank E R 1990 PLTMG: A Software Package for Solving Elliptic Partial Differential Equations (Philadelphia, PA: SIAM)
6. Banks T H and Kunisch K 1989 Estimation Techniques for Distributed Parameter Systems (Boston: Brikhaüser)
7. Barber D and Brown B 1986 Recent developments in applied potential tomography-APT Information Processing in Medical Imaging ed S Bacharach (Amsterdam: Nijhoff) pp 106-21
8. Bensoussan A, Lions J L and Papanicolaou G C 1978 Asymptotic Analysis for Periodic Structures (Amsterdam: North-Holland)
9. Berryman J G 1990 Stable iterative reconstruction algorithm for nonlinear traveltime tomography Inverse Problems 6 21-42
10. Berryman J G 1989 Weighted least-squares criteria for seismic traveltime tomography IEEE Trans. Geosci. Remote Sensing 27 302-9
11. Berryman J G 1989 Fermat's principle and nonlinear traveltime tomography Phys. Rev. Lett. 62 2953-6
12. Berryman J G 1991 Convexity properties of inverse problems with variational constraints J. Franklin Instit. 328 1-13
13. Borcea L and Papanicolaou G C 1996 Network approximation for transport properties of high contrast materials SIAM Appl. Math. at press
14. Borcea L and Papanicolaou G C 1996 A hybrid numerical method for high contrast conductivity problems J. Comput. Appl. Math. submitted
15. Borcea L, Papanicolaou G C and Wehr J Network approximation for high contrast random conductivities, in preparation
16. Curtis E B and Morrow J A 1990 Determining the resistors in a network SIAM J. Appl. Math. 50 931-41
17. Daily W D, Ramirez D, LaBreque D and Nitao J 1992 Electrical resistivity tomography of vadose water movenent Water Resources Res. 28 1429-42
18. Dennis J E and Schnabel R B 1996 Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Philadelphia. PA: SIAM)
19. Dines K A and Lytle R J 1981 Analysis of electrical conductivity imaging Geophysics 46 1025-36
20. Fletcher R 1987 Practical Methods of Optimization (New York: Wiley)
21. Gill P E, Murray W and Wright M H 1981 Practical Optimization (London: Academic)
22. Hebashy T M, Groom R W and Spies B R 1993 Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering J. Geophys. Res. 98 1759-55
23. Hestenes M R and Stiefel E 1952 Methods of conjugate gradients for solving linear systems J. Res. NBS 49 409-36
24. Isakov V 1993 Uniqueness and stability in multi-dimensional inverse problems Inverse Problems 9 579-621
25. Ito K and Kunisch K 1990 The augmented Lagrangian method for parameter estimation in elliptic systems SIAM J. Control 28 113-36
26. Jikov V V, Kozlov S M and Oleinik O A 1994 Homogenization of Differential Operators and Integral Functional (Berlin: Springer)
27. Kaczmarz S 1937 Angenäherte auflösung von systemen linearer gleichungen Bull. Acad. Polon. Sci. Lett. A 35 355-7
28. Kitanidis P K 1995 Quasilinar geostatistical theory for inversing Water Resources Res. 31 2411-19
29. Kohn R and Vogelius M 1985 Determining conductivity by boundary measurements Commun. Pure Appl. Math. 38 643-67
30. Kozlov S M 1989 Geometric aspects of averaging Russian Math. Surveys 44 91-144
31. 1992 LAPACK User's Guide (Philadelphia, PA: SIAM)
32. Levenberg K 1944 A method for the solution of certain non-linear problems in least squares Q. Appl. Math. 2 164-8
33. Lu Shin-yee and Berryman J G 1990 Inverse scattering, seismic traveltime tomography, and neural networks Int. J. Imaging Syst. Technol. 2 112-18
34. Marquardt D W 1963 An algorithm for least-squares estimation of nonlinear parameters SIAM J. Appl. Math. 11 431-41
35. Marquardt D W 1970 Generlized inverses, ridge regression, biased linear estimation, and nonlinear estimation Technometrics 12 591-612
36. Mallat S and Zhang Z 1993 Matching pursuit in a time-frequency dictionary IEEE Trans. Signal Process. 41 3397-415
37. McCormick S F and Wade J G 1993 Multigrid solution of a linearized, regularized least-squares problem in electrical impedance tomography Inverse Problems 9 697-713
38. Mitchell A R 1969 Computational Methods in Partial Differential Equations (New York: Wiley)
39. Natterer F 1986 The Mathematics of Computerized Tomography (New York: Wiley)
40. Ramirez A, Daily D W. LaBrecque D, Owen E and Chesnut D 1993 Monitoring an underground steam injection process using electrical resistance tomography Water Resources Res. 29 73-87
41. Rector J W (ed) 1995 Geophysics 60 Specal issue on Crosswell methods
42. Santosa F and Vogelius M 1990 A backprojection algorithm for electrical impedance imaging SIAM J. Appl. Math. 50 216-43
43. Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem Ann. Math. 125 153-69
44. Sylvester J and Uhlmann G 1990 The Dirichlet to Neumann map - and applications Inverse problems in Partial Differential Equations ed D Colton, R Ewing and W Rundell (Philadelphia, PA: SIAM) pp 101-39
45. Tikhonov A and Arsénine V 1976 Méthodes de Résolution de Problèmes Mal Posés (Moscow: Mir)
46. Yorkey T J, Webster J G and Tompkins W J 1987 Comparing reconstruction algorithms for electrical impedance tomography IEEE Trans. Biomed. Engng 34 843-52
47. Zhou Q, Becker A and Morrison H F 1993 Audio-frequcncy electromagnetic tomography in 2-D Geophysics 58 482-95