Nonlinear Inverse Problems in Imaging

Nonlinear Inverse Problems in Imaging

Volumn , Issue , 2012, Pages

  Seo, Jin Keun ^a   Woo, Eung Je ^b  

^a Yonsei University   (South Korea)

^b Kyung Hee University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891583543     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118478141     Document Type: Book

References (366)

1. Hadamard J 1902 Sur les problémes aux dérivées partielles et leur signification physique. Bull. Univ. Princeton, 13, 49-52.
2. Bracewell R 1999 The Fourier Transform and Its Applications, 3rd edn. McGraw-Hill, New York.
3. Gasquet C and Witomski P 1998 Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets. Springer, New York.
4. Rudin W 1970 Real and Complex Analysis. McGraw-Hill, New York.
5. Strang G 2005 Linear Algebra and Its Applications, 4th edn. Thomson Learning, London.
6. Strang G 2007 Computational Science and Engineering. Wellesley-Cambridge, Wellesley, MA.
7. Evans LC 2010 Partial Differential Equations. Graduate Studies in Mathematics, no. 19. American Mathematical Society, Providence, RI.
8. Gilbarg D and Trudinger N 2001 Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
9. John F 1982 Partial Differential Equations. Applied Mathematical Sciences, vol. 1. Springer, New York.
10. Lieb EH and Loss M 2001 Analysis, 2nd edn. Graduate Studies in Mathematics, no. 14. American Mathematical Society, Providence, RI.
11. Marsden JE 1974 Elementary Classical Analysis. W. H. Freeman, San Francisco.
12. Strauss W A 1992 Partial Differential Equations, An Introduction. John Wiley & Sons, Inc., New York.
13. Akoka S, Franconi F, Seguin F and le Pape A 2009 Radiofrequency map of an NMR coil by imaging. Magn. Reson. Imag. 11, 437-441.
14. Chipot M 2009 Elliptic Equations: An Introductory Course. Birkḧauser Advanced Texts. Birkḧauser, Basel. Engl HW, Hanke M and Neubauer A 1996 Regularization of Inverse Problems. Mathematics and Its Applications. Kluwer Academic, Dordrecht.
15. Feldman J and Uhlmann G 2003 Inverse Problems. Lecture Note. See http://www.math.ubc.ca/~feldman/ibook/.
16. Gilbarg D and Trudinger N 2001 Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
17. Lieb EH and Loss M 2001 Analysis, 2nd edn. Graduate Studies in Mathematics, no. 14. American Mathematical Society, Providence, RI.
18. Marsden JE 1974 Elementary Classical Analysis. W. H. Freeman, San Francisco.
19. Rudin W 1970 Real and Complex Analysis. McGraw-Hill, New York.
20. Stollberger R and Wach P 1996 Imaging of the active B1 field in vivo. Magn. Reson. Med. 35, 246-251.
21. Wheeden RL and Zygmund A 1977 Measure and Integral: An Introduction to Real Analysis. Monographs and Textbooks in Pure and Applied Mathematics, vol. 43. Marcel Dekker, New York.
22. Allen MB, Herrera I and Pinder GF 1988 Numerical Modeling in Science and Engineering. John Wiley & Sons, Inc., New York.
23. Haberman R 1987 Elementary Applied PDEs, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ.
24. Johnson C 2009 Numerical Solution of Partial Differential Equations by the Finite Element Method. Reprint of 1987 edition. Dover, Mineola, NY.
25. Lax PD and Richtmyer RD 1956 Survey of the stability of linear finite difference equations. Commun. Pure Appl. Math. 9, 267-293.
26. Aubert G and Kornprobst P 2002 Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd edn. Applied Mathematical Sciences Series, vol. 147. Springer, New York.
27. Barron JL, Fleet DJ and Beauchemin SS 1994 Performance of optical flow techniques. Int. J. Comput. Vision 12(1), 43-77.
28. Beer 1852 Bestimmung der Absorption des rothen Lichts in farbigen Flussigkeiten. Ann. Phys. Chem. 86, 78-88.
29. Bracewell RN 1956 Strip integration in radioastronomy. J. Phys. 9, 198-217.
30. Bracewell RN and Riddle AC 1967 Inversion of fan-beam scans in radio-astronomy. Astrophys. J. 150, 427-434.
31. Brooks RA and Chiro GD 1976 Beam hardening in x-ray reconstructive tomography. Phys. Med. Biol. 21, 390-398.
32. Bydder M, Larkman DJ and Hajnal JV 2002 Generalized SMASH imaging. Magn. Reson. Med. 47, 160-170.
33. Calder J and Mansouri A 2011 Anisotropic image sharpening via well-posed Sobolev gradient flows. SIAM J. Math. Anal. 43, 1536-1556.
34. Candés EJ and Tao T 2005 Decoding by linear programming. IEEE Trans. Inform. Theory 51(12), 4203-4215.
35. Candés EJ and Tao T 2006 Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inform. Theory 52, 5406-5425.
36. Candés EJ, Romberg J and Tao T 2006a Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52(2), 489-509.
37. Candés EJ, Romberg JK and Tao T 2006b Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59, 1207-1223.
38. Canny JA 1986 Computational approach to edge detection. IEEE Trans. Pattern Anal. Machine Intell. 8(6), 679-698.
39. Caselles V, Catte F, Coll T and Dibos F 1993 A geometric model for active contours in image processing. Numer. Math. 66(1), 1-31.
40. Caselles V, Kimmel R and Sapiro G 1997 Geodesic active contours. Int. J. Comput. Vision 22(1), 61-79.
41. Chan TF and Vese LA 2001 Active contours without edges. IEEE Trans. Image Process. 10(2), 266-277.
42. Chen Y, Tagare HD, Thiruvenkadam S, Huang F, Wilson D, Gopinath KS, Briggs RW and Geiser EA 2002 Using prior shapes in geometric active contours in a variational framework. Int. J. Comput. Vision 50(3), 315-328.
43. Cormack AM 1963 Representation of a function by its line integrals, with some radiological applications. J. Appl. Phys. 34, 2722-2727.
44. Cormack AM 1992 75 years of radon transform. J. Comput. Assist. Tomogr. 16, 673.
45. Damadian RV 1971 Tumor detection by nuclear magnetic resonance. Science 171, 1151-1153.
46. Donoho DL and Elad M 2003 optimally sparse representation in general (non-orthogonal) dictionaries via 1 minimization. Proc. Natl Acad. Sci. USA 100, 2197-2202.
47. Donoho DL and Huo X 1999 Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47, 2845-2862.
48. Duan Q, Angelini ED, Herz SL, Ingrassia CM, Costa KD, Holmes JW, Homma S and Laine AF 2009 Region-based endocardium tracking on real-time three-dimensional ultrasound. Ultrasound Med. Biol. 35(2), 256-265.
49. Faridani A 2003 Introduction to the mathematics of computed tomography. In Inside Out: Inverse Problems and Applications (ed. G Uhlmann). Math. Sci. Res. Inst. Publications, vol. 47, pp. 1-46. Cambridge University Press, Cambridge.
50. Feldkamp LA, Davis LC and Kress JW 1984 Practical cone-beam algorithm. J. Opt. Soc. Am. A 1(6), 612-619.
51. Filler AG 2010 The history, development, and impact of computed imaging in neurological diagnosis and neurosurgery: CT, MRI, DTI Internet J. Neurosurg. 7(1).
52. Goldenberg R, Kimmel R, Rivlin E and Rudzsky M 2001 Fast geodesic active contours. IEEE Trans. Image Process. 10(10), 1467-1475.
53. Grangeat P 1991 Mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform. In Mathematical Methods in Tomography (Oberwolfach, 1990). Lecture Notes in Mathematics, no. 1497, pp. 66-97. Springer, Berlin.
54. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B and Haase A 2002 Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn. Reson. Med. 47, 1202-1210.
55. Haacke E, Brown R, Thompson M and Venkatesan R 1999 Magnetic Resonance Imaging Physical Principles and Sequence Design. John Wiley & Sons, Inc., New York.
56. Heidemann RM, Griswold MA, Haase A and Jakob PM 2001 VD-AUTO-SMASH imaging. Magn. Reson. Med. 45, 1066-1074.
57. Horn B and Schunk B 1981 Determining optical flow. Artif. Intell. 17(2), 185-203.
58. Hounsfield GN 1973 Computerized transverse axial scanning (tomography): I. Description of system. Br. J. Radiol. 46, 1016-1022.
59. Jakob PM, Griswold MA, Edelman RR and Sodickson DK 1998 AUTO-SMASH: a self-calibrating technique for SMASH imaging. Magn. Reson. Mater. Phys., Biol. Med. 7, 42-54.
60. Kak AC and Slaney M 1988 Principles of Computerized Tomographic Imaging. IEEE Press, New York.
61. Kalender WA 2006 X-ray computed tomography. Phys. Med. Biol. 51, R29-R43.
62. KalenderWA, Hebel R and Ebersberger J 1987 Reduction of CT artifacts caused by metallic implants. Radiology 164(2), 576-577.
63. Kass M, Witkin A and Terzopoulos D 1987 Snake: active contour models. Int. J. Comput. Vision 1, 321-331.
64. Kichenassamy S 1997 The Perona-Malik paradox. SIAM J. Appl. Math. 57(5), 1328-1342.
65. Kichenassamy S, Kumar A, Olver P, Tannenbaum A and Yezzi A 1995 Gradient flows and geometric active contour models. In Proc. 5th Int. Conf. on Computer Vision, pp. 810-815. IEEE Press, New York.
66. Kyriakos WE, Panych LP, Kacher DF, Westin CF, Bao SM, Mulkern RV and Jolesz FA 2000 Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP). Magn. Reson. Med. 44, 301-308.
67. Lambert JH 1760 Photometria, sive de Mensura et gradibus luminis,colorum et umbrae. Eberhardt Klett, Augsburg.
68. Larkman DJ and Nunes RG 2001 Parallel magnetic resonance imaging. Phys. Med. Biol. 52, R15.
69. Lauterbur PC 1973 Image formation by induced local interactions: examples of employing nuclear magnetic resonance. Nature 242(5394), 190-191.
70. Lauterbur PC 1974 Magnetic resonance zeugmatography. Pure Appl. Chem. 40, 149-157.
71. Leung KY, Danilouchkine MG, Stralen MV, Jong NE, Steen AFVD and Bosch JG 2011 Left ventricular border tracking using cardiac motion models and optical flow. Ultrasound Med. Biol. 37(4), 605-616.
72. Linguraru MG, Vasilyev NV, Marx GR, Tworetzky W, Nido PJD and Howe RD 2008 Fast block flow tracking of atrial septal defects in 4D echocardiography. Med. Image Anal. 12(4), 397-412.
73. Lucas B and Kanade T 1981 An iterative image restoration technique with an application to stereo vision. Proc. DARPA Image Understanding Workshop, pp. 121-130.
74. Lustig M, Donoho DL and Pauly JM 2007 Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58, 1182-1195.
75. Malladi R, Sethian JA and Vemuri BC 1995 Shape modeling with front propagation: a level set approach. IEEE Trans. Pattern Anal. Machine Intell. 17(2), 158-175.
76. Meyer Y Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, vol. 22. American Mathematical Society, Providence, RI.
77. Meyer E, Raupach R, Lell M, Schmidt B and Kachelrie M 2010 Normalized metal artifact reduction (NMAR) in computed tomography. Med. Phys. 37, 5482-5493.
78. Natterer F 2008 X-Ray Tomography, Inverse Problems and Imaging. Lecture Notes in Mathematics, no. 1943, pp. 17-34. Springer, Berlin.
79. Osher S, Solé A and Vese L 2002 Image decomposition and restoration using total variation minimization and the H -1 norm. SIAM Multiscale Model. Simul. 1(3), 349-370.
80. Osher S, Burger M, Goldfarb D, Xu J and Yin W 2005 An iterative regularization method for total variationbased image restoration. SIAM Multiscale Model. Simul. 4(2), 460-489.
81. Paragios N and Deriche R 1998 A PDE-based level set approach for detection and tracking of moving objects. In Proc. 6th Int. Conf. on Computer Vision, pp. 1139-1145. IEEE, New York.
82. Perona P and Malik J 1990 Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12, 629-639.
83. Pruessmann KP, Weiger M, Scheidegger MB and Boesiger P 1999 SENSE: sensitivity encoding for fast MRI. Magn. Reson. Med. 42, 952-962.
84. Pruessmann KP, Weiger M, Bornert P and Boesiger P 2001 Advances in sensitivity encoding with arbitrary k-space trajectories. Magn. Reson. Med. 46, 638-651.
85. Radon JH 1917 Ü ber die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Ber. S̈achs. Akad. Wiss. (Leipzig) 69, 262-277.
86. Rudin L, Osher SJ and Fatemi E 1992 Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268.
87. Sarti A, Corsi C, Mazzini E and Lamberti C 2005 Maximum likelihood segmentation of ultrasound images with Rayleigh distribution. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(6), 947-960.
88. Sodickson DK and Manning WJ 1997 Simultaneous acquisition of spatial harmonics (SMASH): fast imaging withradiofrequency coil arrays. Magn. Reson. Med. 38, 591-603.
89. Sodickson DK, Griswold MA, Jakob PM, Edelman RR and Manning WJ 1999 Signal-to-noise ratio and signal-to-noise efficiency in SMASH imaging. Magn. Reson. Med. 41, 1009-1022.
90. Suhling M, Arigovindan M, Jansen C, Hunziker P and Unser M 2005 Myocardial motion analysis from B-mode echocardiograms. IEEE Trans. Image Process. 14(4), 525-536.
91. Tuy HK 1983 An inversion formula for cone-beam reconstruction. SIAM J. Appl. Math. 43, 546-552.
92. Veronesi F, Corsi C, Caiani EG, Sarti A and Lamberti C 2006 Tracking of left ventricular long axis from real-time three-dimensional echocardiography using optical flow techniques. IEEE Trans. Inform. Technol. Biomed. 10(1), 174-181.
93. Vese L and Osher S 2002 Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput. 19, 553-572.
94. Wang G, Snyder DL, O'Sullivan JA and Vannier MW 1996 Iterative deblurring for CT metal artifact reduction. IEEE Trans. Med. Imag. 15, 657-664.
95. Weickert J 1997 A review of nonlinear diffusion filtering. In Scale-Space Theory in Computer Vision (eds BtH Romeny, L Florack, J Koenderink and M Viergever). Lecture Notes in Computer Science, no. 1252, pp. 3-28. Springer, Berlin.
96. Yezzi A, Tsai A and Willsky A 1999 Binary and ternary flows for image segmentation. In Proc. Int. Conf. on Image Processing, vol. 2, pp. 1-5. IEEE, New York.
97. You Y, Xu W, Tannenbaum A and Kaveh M 1996 Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5, 15-53.
98. Adler A and Lionheart W 2006 Uses and abuses of EIDORS: an extensible software base for EIT. Physiol. Meas. 27(5), S25-S42.
99. Alessandrini G 1988 Stable determination of conductivity by boundary measurements. Appl. Anal. 27, 153-172.
100. Astala K and Paivarinta L 2006a A boundary integral equation for Calderón's inverse conductivity problem. In Proc. 7th Int. Conf. on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain, June 2004 ; Collect. Math., Extra Volume, pp. 127-139.
101. Astala K and Paivarinta L 2006b Calderón's inverse conductivity problem in the plane. Ann. Math. 163, 265-299.
102. Barber DC and Brown BH 1983 Imaging spatial distribution of resistivity using applied potential tomography. Electron. Lett. 19, 933-935.
103. Barber DC and Brown BH 1984 Applied potential tomography. J. Phys. E: Sci. Instrum. 17, 723-733.
104. Barber DC and Brown BH 1988 Errors in reconstruction of resistivity images using a linear reconstruction technique. Clin. Phys. Physiol. Meas. 9, 101-104.
105. Berenstein CA, Tarabusi EC, Cohen JM and Picardello MA 1991 Integral geometry on trees. Am. J. Math. 113, 441-470.
106. Boone K, Barber DC and Brown BH 1997 Imaging with electricity: report of the European Concerted Action on Impedance Tomography. J. Med. Eng. Technol. 21, 201-232.
107. Brown R and Uhlmann G 1997 Uniqueness in the inverse conductivity problem with less regular conductivities in two dimensions. Commun. PDE 22, 1009-1027.
108. Brown BH, Barber DC and Seagar AD 1985 Applied potential tomography: possible clinical applications. Clin. Phys. Physiol. Meas. 6, 109-121.
109. Bujnowski A and Wtorek J 2007 An excitation in differential EIT selection of measurement frequencies. In Proc. 13th Int. Conf. on Electrical Bioimpedance and 8th Conf. on Electrical Impedance Tomography, Graz, Austria, 29 August-2 September. IFMBE Proceedings, vol. 17, eds. H. Scharfetter and R. Merwa. Springer, Berlin.
110. Calderón AP 1980 On an inverse boundary value problem. Seminar on Numerical Analysis and its Applications to Continuum Physics, pp. 65-73.
111. Cheney M, Isaacson D and Isaacson EL 1990 Exact solutions to a linearized inverse boundary value problem. Inv. Prob. 6, 923-934.
112. Cheney M, Isaacson D, Isaacson E, Somersalo E and Coffey EJ 1991 A layer-stripping reconstruction algorithm for impedance imaging. In Proc. 13th Annu. Int. Conf. IEEE Engineering in Medicine and Biology Society, pp. 2-4. IEEE, New York.
113. Cheney M, Isaacson D and Newell JC 1999 Electrical impedance tomography. SIAM Rev. 41, 85-101.
114. Cheng KS, Isaacson D, Newell JC and Gisser DG 1989 Electrode models for electric current computed tomography. IEEE Trans. Biomed. Eng. 36(9), 918-924.
115. Cherkaeva E and Cherkaev A 1995 Bounds for detectability of material damage by noisy electrical measurements. In Structural and Multidisciplinary Optimization, eds N Olhoff and GIN Rozvany, pp. 543-548. Pergamon, Oxford.
116. Cohen-Bacrie C, Goussard Y and Guardo R 1997 Regularized reconstruction in electrical impedance tomography using a variance uniformization constraint. IEEE Trans. Biomed. Imag. 6, 562.
117. Cook RD, Saulnier GJ, Gisser DG, Goble JC, Newell JC and Isaacson D 1994 ACT3: a high-speed, highprecision electrical impedance tomograph. IEEE Trans Biomed Eng. 41(8), 713-722.
118. Edic PM, Isaacson D, Saulnier GJ, Jain H and Newell JC 1998 An iterative Newton-Raphson method to solve the inverse admittivity problem. IEEE Trans. Biomed. Eng. 45, 899-908.
119. Faddeev D 1965 Growing solutions of the Schr̈odinger equation. Sov. Phys. Dokl. 10, 1033 (Engl. transl.).
120. Fitzgerald A, Holder D and Griffiths H 1999 Experimental assessment of phase magnitude imaging in multifrequency EIT by simulation and saline tank studies. Ann. NY Acad. Sci. 873, 381-387.
121. Fuks LF, Cheney M, Isaacson D, Gisser DG and Newell JC 1991 Detection and imaging of electric conductivity and permittivity at low frequency. IEEE Trans Biomed Eng. 38(11), 1106-1110.
122. Gabriel C, Gabriel S and Corthout E 1996a The dielectric properties of biological tissues: I. Literature survey. Phys. Med. Biol. 41, 2231-2249.
123. Gabriel S, Lau RW and Gabriel C 1996b The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys. Med. Biol. 41, 2251-2269.
124. Geddes LA and Baker LE 1967 The specific resistance of biological material: a compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. 5, 271-293.
125. Gisser DG, Isaacson D and Newell JC 1988 Theory and performance of an adaptive current tomograph system. Clin. Phys. Physiol. Meas. 9 (Suppl. A), 35-41.
126. Gisser DG, Isaacson D and Newell JC 1990 Electric current computed tomography and eigenvalues. SIAM J. Appl. Math. 50, 1623-1634.
127. Griffiths H 1987 The importance of phase measurement in electrical impedance tomography. Phys. Med. Biol. 32, 1435-1444.
128. Griffiths H and Ahmed A 1987a A dual-frequency applied potential tomography technique: computer simulations. Clin. Phys. Physiol. Meas. 8, 103-107.
129. Griffiths H and Ahmed A 1987b Electrical impedance tomography for thermal monitoring of hyperthermia treatment: an assessment using in vitro and in vivo measurements. Clin. Phys. Physiol. Meas. 8, 141-146.
130. Griffiths H and Zhang Z 1989 A dual-frequency electrical impedance tomography system. Phys. Med. Biol. 34, 1465-1476.
131. Grimnes S and Martinsen OG 2008 Bioimpedance and Bioelectricity Basics, 2nd edn. Academic Press, Oxford.
132. Holder D (ed.) 2005 Electrical Impedance Tomography: Methods, History and Applications. IOP Publishing, Bristol.
133. Hyaric AL and Pidcock MK 2001 An image reconstruction algorithm for three-dimensional electrical impedance tomography. IEEE Trans. Biomed. Eng. 48, 230-235.
134. Isaacson D and Cheney M 1991 Effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms. SIAM J. Appl. Math. 15, 1705-1731.
135. Isaacson D, Newell JC and Gisser DG 1989 Rapid assessment of electrode characteristics for impedance imaging. In Proc. 11th Annu. Int. Conf. IEEE Engineering in Medicine and Biology Society, pp. 474-475. IEEE, New York.
136. Isaacson D, Blue RS and Newell JC 1996 A 3-D impedance imaging algorithm for multiple layers of electrodes. In Proc. Association for the Advancement of Medical Instrumentation Conf.
137. Isakov V 1991 Completeness of products of solutions and some inverse problems for PDE. J. Differ. Eqns 92, 305-317.
138. Kenig CE, Sjostrand J and Uhlmann G 2007 The Calderón problem with partial data. Ann. Math. 165, 567-591.
139. Kohn R and Vogelius M 1984 Identification of an unknown conductivity by means of measurements at the boundary. In Inverse Problems. SIAM-AMS Proceedings, vol. 14, pp. 113-123.
140. Kohn R and Vogelius M 1985 Determining conductivity by boundary measurements: II. Interior results. Commun. Pure Appl. Math. 38, 643-667.
141. Kolehmainen V, Lassas M and Ola P 2005 The inverse conductivity problem with an imperfectly known boundary. SIAM J. Appl. Math. 66, 365-383.
142. Kulkarni R, Boverman G, Isaacson D, Saulnier GJ, Kao TJ and Newell JC 2008 An analytical layered forward model for breasts in electrical impedance tomography. Physiol. Meas. 29, S27-S40.
143. Lionheart W, Polydorides N and Borsic A 2005 The reconstruction problem. In Electrical Impedance Tomography: Methods, History and Applications, ed. D Holder. IOP Publishing, Bristol.
144. McEwan A, Romsauerova A, Yerworth R, Horesh L, Bayford R and Holder D 2006 Design and calibration of a compact multi-frequency EIT system for acute stroke imaging. Physiol. Meas. 27, S199-S210.
145. Mueller JL and Siltanen S 2003 Direct reconstructions of conductivities from boundary measurements. SIAM J. Sci. Comput.tion 24(4), 1232-1266.
146. Murphy EK and Mueller JL 2009 Effect of domain-shape modeling and measurement errors on the 2-D D-bar method for electrical impedance tomography. IEEE Trans. Med. Imag. 28(10), 1576-1584.
147. Nachman A 1988 Reconstructions from boundary measurements. Ann. Math. 128, 531-576.
148. Nachman A, Sylvester J and Uhlmann G 1988 An n-dimensional Borg-Levinson theorem. Commun. Math. Phys. 115, 593-605.
149. Newell JC, Gisser DG and Isaacson D 1988 An electric current tomograph. IEEE Trans. Biomed. Eng. 35, 828-833.
150. Nissinen A, Heikkinen LM and Kaipio JP 2008 The Bayesian approximation error approach for electrical impedance tomography - experimental results. Meas. Sci. Technol. 19, 015501.
151. Oh TI, Woo EJ and Holder D 2007a Multi-frequency EIT system with radially symmetric architecture: KHU Mark1. Physiol. Meas. 28, S183-S196.
152. Oh TI, Lee KH, Kim SM, Koo H, Woo EJ and Holder D 2007b Calibration methods for a multi-channel multi-frequency EIT system. Physiol. Meas. 28, S1175-S1188.
153. Oh TI, Koo W, Lee KH, Kim SM, Lee J, Kim SW, Seo JK and Woo EJ 2008 Validation of a multi-frequency electrical impedance tomography (mfEIT) system KHU Mark1: impedance spectroscopy and time-difference imaging. Physiol. Meas. 29, S295-S307.
154. Romsauerova A, McEwan A, Horesh L, Yerworth R, Bayford RH and Holder D 2006a Multi-frequency electrical impedance tomography (EIT) of the adult human head: initial findings in brain tumours, arteriovenous malformations and chronic stroke, development of an analysis method and calibration. Physiol. Meas. 27, S147-S161.
155. Romsauerova A, McEwan A and Holder DS 2006b Identification of a suitable current waveform for acute stroke imaging. Physiol. Meas. 27, S211-S219.
156. Santosa F and Vogelius M 1990 A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math. 50, 216-243.
157. Saulnier GJ 2005 EIT instrumentation. In Electrical Impedance Tomography: Methods, History and Applications, ed. DS Holder. IOP Publishing, Bristol.
158. Schlappa J, Annese E and Griffiths H 2000 Systematic errors in multi-frequency EIT. Physiol. Meas. 21, S111-S118.
159. Seo JK, Lee J, Kim SW, Zribi H and Woo EJ 2008 Frequency-difference electrical impedance tomography (fdEIT): algorithm development and feasibility study. Physiol. Meas. 29, S929-S944.
160. Siltanen S, Mueller JL, Isaacson D 2000 An implementation of the reconstruction algorithm of A Nachman for the 2-D inverse conductivity problem. Inv. Probs 16, 681-699.
161. Somersalo E, Cheney M, Isaacson D and Isaacson E 1991 Layer stripping: a direct numerical method for impedance imaging. Inv. Prob. 7, 899-926.
162. Somersalo E, Cheney M and Isaacson D 1992 Existence and uniqueness for electrode models for electric current computed tomography. SIAM J. Appl. Math. 52, 1023-1040.
163. Soni NK, Hartov A, Kogel C, Poplack SP and Paulsen KD 2004 Multi-frequency electrical impedance tomography of the breast: new clinical results. Physiol. Meas. 25, S301-S314.
164. Sylvester J and Uhlmann G 1986 A uniqueness theorem for an inverse boundary value problem in electrical prospection. Commun. Pure Appl. Math. 39, 92-112.
165. Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125, 153-165.
166. Sylvester J and Uhlmann G 1988 Inverse boundary value problems at the boundary - continuous dependence. Commun. Pure Appl. Math. 41, 197-221.
167. Trokhanova OV, Okhapkin MB and Korjenevsky AV 2008 Dual-frequency electrical impedance mammography for the diagnosis of non-malignant breast disease. Physiol. Meas. 29, S331-S334.
168. Vauhkonen PJ, Vauhkonen M, Savolainen T and Kaipio JP 1996 Three-dimensional electrical impedance tomography based on the complete electrode model. IEEE Trans. Biomed. Eng 45, 1150-1160.
169. Vauhkonen M, Vadasz D, Karjalainen PA, Somersalo E and Kaipio JP 1998 Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans. Med. Imag. 17, 285-293.
170. Wexler A, Fry B and Neuman MR 1985 Impedance-computed tomography algorithm and system. Appl. Opt. 24, 3985-3992.
171. Wilson AJ, Milnes P, Waterworth AR, Smallwood RH and Brown BH 2001 Mk3.5: a modular, multi-frequency successor to the Mk3a EIS/EIT system. Physiol. Meas. 22, S49-S54.
172. Woo EJ, Hua P, Tompkins WJ and Webster JG 1993 A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography. IEEE Trans. Med. Imag. 12(2), 137-146.
173. Yerworth RJ, Bayford RH, Brown B, Milnes P, Conway M and Holder DS 2003 Electrical impedance tomography spectroscopy (EITS) for human head imaging. Physiol. Meas. 24, S477-S489.
174. Yorkey JT 1987 Personal communication (Lawrence Livermore National Laboratory, Livermore, CA, USA).
175. Yorkey TJ and Webster JG 1987 A comparison of impedance tomographic reconstruction algorithms. Clin. Phys. Physiol. Meas. 8 (Suppl. A), 55-62.
176. Adler A, Arnold JH, Bayford R, Borsic A, Brown B, Dixon P, Faes TJC, Frerichs I, Gagnon H, G̈arber Y,
177. Grychtol B, Hahn G, Lionheart WRB, Malik A, Patterson RP, Stocks J, Tizzard A, Weiler N and Wolf GK 2009 GREIT: a unified approach to 2D linear EIT reconstruction of lung images. Physiol. Meas. 30, S35-S55.
178. GK 2009 GREIT: a unified approach to 2D linear EIT reconstruction of lung images. Physiol. Meas. 30, S35-S55.
179. Alessandrini G and Magnanini R 1992 The index of isolated critical points and solutions of elliptic equations in the plane. Ann. Scu. Norm. Sup. Pisa Cl. Sci. 19, 567-589.
180. Alessandrini G, Isakov V and Powell J 1995 Local uniqueness in the inverse problemwith one measurement. Trans. Am. Math. Soc. 347, 3031-3041.
181. Ammari H and Seo JK 2003 An accurate formula for the reconstruction of conductivity inhomogeneity. Adv. Appl. Math. 30, 679-705.
182. Ammari H, Moskow S and Vogelius MS 2003 Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM: Control Optim. Calc. Var. 9, 49-66.
183. Astala K and P̈aiv̈arinta L 2006 Calderon's inverse conductivity problem in the plane. Ann. Math. 163, 265-299.
184. Barber DC and Brown BH 1984 Applied potential tomography. J. Phys. Sci. Instrum. 17 723-733.
185. Bellout H and Friedman A 1988 Identification problem in potential theory. Arch. Rat. Mech. Anal. 101, 143-160.
186. Bellout H, Friedman A and Isakov V 1992 Inverse problem in potential theory. Trans. Am. Math. Soc. 332, 271-296.
187. Berenstein C and Tarabusi EC 1991 Inversion formulas for the k-dimensional Radon transform in real hyperbolic spaces. Duke Math. J. 62, 1-9.
188. Boone K, Barber D and Brown B 1997 Imaging with electricity: report of the European Concerted Action on Impedance Tomography. J. Med. Eng. Technol. 21(6), 201-202.
189. Brown R and Uhlmann G 1997 Uniqueness in the inverse conductivity problem with less regular conductivities in two dimensions. Commun. Part. Differ. Eqns 22, 1009-1027.
190. Brown BH, Barber DC and Seagar AD 1985 Applied potential tomography: possible clinical applications. Clin. Phys. Physiol. Meas. 6, 109-121.
191. Br̈uhl M and Hanke M 2000 Numerical implementation of two non-iterative methods for locating inclusions by impedance tomography. Inv. Prob. 16, 1029-1042.
192. Bryan K 1991 Numerical recovery of certain discontinuous electrical conductivities. Inv. Prob. 7, 827-840.
193. Calderón AP 1980 On an inverse boundary value problem. In Seminar on Numerical Analysis and its Applications to Continuum Physics, pp. 65-73. Sociedade Brasileira de Matemática, Rio de Janeiro.
194. Cedio-Fengya DJ, Moskow S and Vogelius M 1998 Identification of conductivity imperfections of small parameter by boundary measurements. Continuous dependence and computational reconstruction. Inv. Prob. 14, 553-595.
195. Cheney M, Isaacson D, Newell J, Goble J and Simske S 1990 NOSER: an algorithm for solving the inverse conductivity problem. Int. J. Imag. Syst. Technol. 2, 66-75.
196. Cheney M, Isaacson D and Newell JC 1999 Electrical impedance tomography. SIAM Rev. 41, 85-101.
197. Cherepenin V, Karpov A, Korjenevsky A, Kornienko V, Mazaletskaya A, Mazourov D and Meister J 2001 A 3D electrical impedance tomography (EIT) system for breast cancer detection. Physiol. Meas. 22, 9-18.
198. Cherepenin V, Karpov A, Korjenevsky A, Kornienko V, Kultiasov Y, Ochapkin M, Trochanova O and
199. Meister J 2002 Three-dimensional EIT imaging of breast tissues: system design and clinical testing. IEEE Trans. Med. Imag. 21, 662-667.
200. Cohen-Bacrie C and Guardo R 1997 Regularized reconstruction in electrical impedance tomography using a variance uniformization constraint. IEEE Trans. Med. Imag. 16(5), 562-571.
201. Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Springer, Berlin.
202. Cook RD, Saulnier GJ, Gisser DG, Goble JG, Newell JC and Isaacson D 1994 ACT3: a high-speed, highprecision electrical impedance tomography. IEEE Trans. Biomed. Eng. 41, 713-722.
203. Dobson D and Santosa F 1994 An image-enhancement technique for electrical impedance tomography. Inv. Prob. 10, 317-334.
204. Escauriaza L, Fabes E and Verchota G 1992 On a regularity thoerem for weak solutions to transmission problems with internal Lipschitz boundaries. Proc. Am. Math. Soc. 115, 1069-1076.
205. Fabes E, Sand M and Seo JK 1992 The spectral radius of the classical layer potentials on convex domains. IMA Vol. Math. Appl. 42, 129-137.
206. Fabes E, Kang H and Seo JK 1999 Inverse conductivity problem: error estimates and approximate identification for perturbed disks. SIAM J. Math. Anal. 30, 699-720.
207. Feldman J and Uhlmann G 2003 Inverse Problems, Lecture Note. See http://www.math.ubc.ca/~feldman/ibook/.
208. Franco S 2002 Design with Operational Amplifiers and Analog Integrated Circuits, 3rd edn. McGraw-Hill, New York.
209. Friedman A and Isakov V 1989 On the uniqueness in the inverse conductivity problem with one measurement. Indiana Univ. Math. J. 38, 563-579.
210. Friedman A and Vogelius MS 1989 Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence. Arch. Rat. Mech. Anal. 105, 299-326.
211. Fuks LF, Cheney M, Isaacson D, Gisser DG and Newell JC 1991 Detection and imaging of electric conductivity and permittivity at low frequency. IEEE Trans. Biomed. Eng. 3, 1106-1110.
212. Gabriel C, Gabriel S and Corthout E 1996 The dielectric properties of biological tissues: I. Literature survey. Phys. Med. Biol. 41, 2231-2249.
213. Gabriel S, Lau RW and Gabriel C 1996 The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys. Med. Biol. 41, 2251-2269.
214. Geddes LA and Baker LE 1967 The specific resistance of biological material: a compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. 5, 271-293.
215. Giaquinta M 1983 Multiple Integrals in the Calculus of Variations and Non-Linear Elliptic Systems. Princeton University Press, Princeton, NJ.
216. Gilbarg D and Trudinger N 1998 Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
217. Gisser DG, Isaacson D and Newell JC 1988 Theory and performance of an adaptive current tomography system. Clin. Phys. Physiol. Meas. 9 (Suppl. A), 35-41.
218. Gisser DG, Isaacson D and Newell JC 1990 Electric current computed tomography and eigenvalues. SIAM J. Appl. Math. 50, 1623-1634.
219. Grimnes S and Martinsen OG Bioimpedance and Bioelectricity Basics. Academic Press, London.
220. Grisvard P 1985 Elliptic Problems in Nonsmooth Domains. Monographs and Studies in Mathematics, no. 24. Pitman, Boston, MA.
221. Henderson RP and Webster JG 1978 An impedance camera for spatially specific measurements of the thorax. IEEE Trans. Biomed. Eng., 25, 250-254.
222. Hettlich F and Rundell W 1998 The determination of a discontinuity in a conductivity from a single boundary measurement. Inv. Prob. 14, 67-82.
223. Holder D (ed.) 2005 Electrical Impedance Tomography: Methods, History and Applications. IOP Publishing, Bristol.
224. Hua P, Tompkins W and Webster J 1988 A regularized electrical impedance tomography reconstruction algorithm. Clin. Phys. Physiol. Meas. 9, 137-141.
225. Hyaric AL and Pidcock MK 2001 An image reconstruction algorithm for three-dimensional electrical impedance tomography. IEEE Trans. Biomed. Eng. 48(2), 230-235.
226. Ikehata M 2000 On reconstruction in the inverse conductivity problem with one measurement. Inv. Prob. 16, 785-793.
227. Isaacson D 1986 Distinguishability of conductivities by electric current computed tomography. IEEE Trans. Med. Imag. 5(2), 91-95.
228. Isaacson D and Cheney M 1991 Effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms. SIAM J. Appl. Math. 51 1705-1731.
229. Isaacson D and Cheney M 1996 Process for producing optimal current patterns for electrical impedance tomography. US Patent 5588429, 31 December.
230. Isaacson D and Isaacson E 1989 Comment on Calderon's paper: "On an inverse boundary value problem". Math. Comput. 52, 553-559.
231. Isakov V 1988 On uniqueness of recovery of a discontinuous conductivity coefficient. Commun. Pure Appl. Math. 41, 856-877.
232. Isakov V 1998 Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, no. 127. Springer, New York.
233. Lieb EH and Loss M 2001 Analysis, 2nd edn. Graduate Studies in Mathematics, vol. 14. American Mathematical Society, Providence, RI.
234. Kao T, Newell JC, Saulnier GJ and Isaacson D 2003 Distinguishability of inhomogeneities using planar electrode arrays and different patterns of applied excitation. Physiol. Meas. 24, 403-411.
235. Kerner TE, Paulsen KD, Hartov A, Soho SK and Poplack SP 2002 Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects. IEEE Trans. Med. Imag. 21, 638-645.
236. Kellogg OD 1953 Foundations of Potential Theory. Dover, New York.
237. Kohn R and Vogelius M 1984 Determining conductivity by boundary measurements. Commun. Pure Appl. Math. 37, 113-123.
238. Larson-Wiseman JL 1998 Early breast cancer detection utilizing clustered electrode arrays in impedance imaging. PhD Thesis, Rensselaer Polytechnic Institute, Troy, NY.
239. Lionheart W, Polydorides W and Borsic A 2005 The reconstruction problem. In Electrical Impedance Tomography: Methods, History and Applications, ed. DS Holder. IOP Publishing, Bristol.
240. Liu N, Saulnier GJ, Newell JC, Isaacson D and Kao TJ 2005 ACT4: a high-precision, multi-frequency electrical impedance tomography. In Proc. Conf. on Biomedical Applications of Electrical Impedance Tomography, University College London, 22-24 June.
241. Marsden JE 1974 Elementary Classical Analysis. W.H. Freeman, San Francisco.
242. Mast TD, Nachman A and Waag RC 1997 Focusing and imagining using eigenfunctions of the scattering operator. J. Acoust. Soc. Am. 102, 715-725.
243. Metherall P, Barber DC, Smallwood RH and Brown BH 1996 Three-dimensional electrical impedance tomography. Nature 380, 509-512.
244. Mueller JL, Isaacson D and Newell JC 1999 A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays. IEEE Trans. Biomed. Eng. 46, 1379-1386.
245. Nachman A 1988 Reconstructions from boundary measurements. Ann. Math. 128, 531-577.
246. Nachman A 1996 Global uniqueness for a two-dimensional inverse boundary value problem. Ann. Math. 142, 71-96.
247. Newell JC, Gisser DG and Isaacson D 1988 An electric current tomograph. IEEE Trans. Biomed. Eng. 35, 828-833.
248. Oh TI, Lee J, Seo JK, Kim SW and Woo EJ 2007 Feasibility of breast cancer lesion detection using multifrequency trans-admittance scanner (TAS) with 10 Hz to 500 kHz bandwidth. Physiol. Meas. 28, S71-S84.
249. Reed M and Simon B 1980 Methods of Modern Mathematical Physics I: Functional Analysis, revised and enlarged edition. Academic Press, San Diego.
250. Rudin W 1970 Real and complex analysis. McGraw-Hill, New York.
251. Santosa F and Vogelius MS 1990 A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math. 50, 216-243.
252. Scholz B 2002 Towards virtual electrical breast biopsy: space-frequency MUSIC for trans-admittance data. IEEE Trans. Med. Imag. 21, 588-595.
253. Seo JK 1996 On the uniqueness in the inverse conductivity problem. J. Fourier Anal. Appl. 2, 227-235.
254. Seo JK, Lee J, Kim SW, Zribi H and Woo EJ 2008 Frequency-difference electrical impedance tomography (fdEIT): algorithm development and feasibility study. Physiol. Meas. 29, 929-944.
255. Stein EM and Shakarchi R 2005 Real Analysis: Measure Theory, Integration and Hilbert Spaces. Princeton University Press, Princeton, NJ.
256. Sylvester J and Uhlmann G 1986 A uniqueness theorem for an inverse boundary value problem in electrical prospection. Commun. Pure Appl. Math. 39, 91-112.
257. Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125, 153-169.
258. Sylvester J and Uhlmann G 1988 Inverse boundary value problems at the boundary - continuous dependence. Commun. Pure Appl. Math. 21, 197-221.
259. Tidswell AT, Gibson A, Liston A, Yerworth RJ, Bagshaw A, Wyatt J, Bayford RH and Holder DS 2001 3D electrical impedance tomography of neonatal brain activity. In Biomedical Applications of EIT, EPSRC 3rd Engineering Network Meeting, London.
260. Vauhkonen M, Vadasz D, Karjalainen PA, Somersalo E and Kaipio JP 1998 Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans. Med. Imag. 17(2), 285-293. Webster J 1990 Electrical Impedance Tomography. Adam Hilger, Bristol.
261. Wexler A, Fry B and Neuman MR 1985 Impedance-computed tomography algorithm and system. Appl. Opt. 24, 3985-3992.
262. Wheeden RL and Zygmund A 1977 Measure and Integral: An Introduction to Real Analysis. Monographs and Textbooks in Pure and Applied Mathematics, vol. 43. Marcel Dekker, New York.
263. Wilson AJ, Milnes P, Waterworth AR, Smallwood RH and Brown BH 2001 Mk3.5: a modular, multi-frequency successor to the Mk3a EIS/EIT system. Physiol. Meas. 22, 49-54.
264. Woo EJ, Hua P, Webster J and Tompkins W 1993 A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography. IEEE Trans. Med. Imag. 12, 137-146.
265. Yorkey T, Webster J and Tompkins W 1987 Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans. Biomed. Engr. 34, 843-852.
266. Zhang N 1992 Electrical impedance tomography based on current density imaging. MS Thesis, University of Toronto, Canada.
267. Alessandrini G and Magnanini R 1992 The index of isolated critical points and solutions of elliptic equations in the plane. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 19, 567-589.
268. Alessandrini G, Isakov V and Powell J 1995 Local uniqueness in the inverse problem with one measurement. Trans. Am. Math. Soc. 347, 3031-3041.
269. Bauman P, Marini A and Nesi V 2000 Univalent solutions of an elliptic system of partial differential equations arising in homogenization. Indiana Univ. Math. J. 128, 53-64.
270. Bernstein MA, King KF and Zhou XJ 2004 Handbook of MRI Pulse Sequences. Elsevier, Burlington, MA.
271. Birgul O and Ider YZ 1995 Use of the magnetic field generated by the internal distribution of injected currents for electrical impedance tomography. In Proc. 9th Int. Conf. on Electrical Bio-Impedance, Heidelberg, Germany, pp. 418-419.
272. Birgul O and Ider YZ 1996 Electrical impedance tomography using the magnetic field generated by injected currents. In Proc. 18th Annu. Int. Conf. IEEE Engineering in Medicine and Biology Society, Amsterdam, The Netherlands, pp. 784-785. IEEE, New York.
273. Birgul O, Eyuboglu BM and Ider YZ 2003 Experimental results for 2D magnetic resonance electrical impedance tomography (MREIT) using magnetic flux density in one direction. Phys. Med. Biol. 48, 3485-3504.
274. Birgul O, Hamamura MJ, Muftuler T and Nalcioglu O 2006 Contrast and spatial resolution in MREIT using low amplitude current. Phys. Med. Biol. 51, 5035-5049.
275. Folland G 1976 Introduction to Partial Differential Equations. Princeton University Press, Princeton, NJ.
276. Gao G, Zhu SA and He B 2005 Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement. Phys. Med. Biol. 50, 2675-2687.
277. Gao N, Zhu SA and He BA 2006 New magnetic resonance electrical impedance tomography (MREIT) algorithm: the RSM-mREIT algorithm with applications to estimation of human head conductivity. Phys. Med. Biol. 51, 3067-3083.
278. Haacke EM, Brown RW, Thompson MR and Venkatesan R 1999 Magnetic Resonance Imaging: Physical Principles and Sequence Design. John Wiley & Sons, Inc., New York.
279. Hamamura MJ and Muftuler LT 2008 Fast imaging for magnetic resonance electrical impedance tomography. Magn. Reson. Imag. 26, 739-745.
280. Hamamura MJ, Muftuler LT, Birgul O and Nalcioglu O 2006 Measurement of ion diffusion using magnetic resonance electrical impedance tomography. Phys. Med. Biol. 51, 2753-2762.
281. Hasanov KF, Ma AW, Nachman AI and Joy MLG 2008 Current density impedance imaging. IEEE Trans. Med. Imag. 27, 1301-1309.
282. Hedeen RA and Edelstein WA 1997 Characterization and prediction of gradient acoustic noise in MR imagers. Magn. Reson. Med. 37, 7-10.
283. Holder D (ed.) 2005 Electrical Impedance Tomography: Methods, History and Applications. IOP Publishing, Bristol.
284. Ider YZ and Onart S 2004 Algebraic reconstruction for 3D MREIT using one component of magnetic flux density. Physiol. Meas. 25, 281-294.
285. Ider YZ, Onart S and Lionheart WRB 2003 Uniqueness and reconstruction in magnetic resonance electrical impedance tomography (MREIT). Physiol. Meas. 24, 591-604.
286. Jeon K, Lee CO, Kim HJ, Woo EJ and Seo JK 2009a CoReHA: conductivity reconstructor using harmonic algorithms for magnetic resonance electrical impedance tomography (MREIT). J. Biomed. Eng. Res. 30, 279-287.
287. Jeon K, Minhas AS, Kim YT, Jeong WC, Kim HJ, Kang BT, Park HM, Lee CO, Seo JK and Woo EJ 2009b MREIT conductivity imaging of the postmortem canine abdomen using CoReHA. Physiol. Meas. 30, 957-966.
288. Jeong WC, Kim YT, Minhas AS, Kim HJ, Woo EJ and Seo JK 2008 Design of carbon-hydrogel electrode for MREIT. In Proc. 9th Int. Conf. on Electrical Impedance Tomography, Dartmouth, NH.
289. Joy MLG, Scott GC and Henkelman RM 1989 In vivo detection of applied electric currents by magnetic resonance imaging. Magn. Reson. Imag. 7, 89-94.
290. Khang HS, Lee BI, Oh SH, Woo EJ, Lee SY, Cho MH, Kwon O, Yoon JR and Seo JK 2002 J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images. IEEE Trans. Med. Imag. 21, 695-702.
291. Kim HJ, Lee BI, Cho Y, Kim YT, Kang BT, Park HM, Lee SY, Seo JK and Woo EJ 2007 Conductivity imaging of canine brain using a 3T MREIT system: postmortem experiments. Physiol. Meas. 28, 1341-1353.
292. Kim HJ, Oh TI, Kim YT, Lee BI, Woo EJ, Seo JK, Lee SY, Kwon O, Park C, Kang BT and Park HM 2008a In vivo electrical conductivity imaging of a canine brain using a 3T MREIT system. Physiol. Meas. 29, 1145-1155.
293. Kim HJ, Kim YT, Jeong WC, Minhas AS, Woo EJ, Kwon OJ and Seo JK 2008b In vivo conductivity imaging of a human leg using a 3T MREIT system. In Proc. 9th Int. Conf. on Electrical Impedance Tomography, Dartmouth, NH.
294. Kim HJ, Kim YT, Minhas AS, Jeong WC, Woo EJ, Seo JK and Kwon OJ 2009 In vivo high-resolution conductivity imaging of the human leg using MREIT: the first human experiment. IEEE Trans. Med. Imag. 28, 1681-1611.
295. Kim YT, Yoo PJ, Oh TI and Woo EJ 2011 Magnetic flux density measurement in magnetic resonance electrical impedance tomography using a low-noise current source. Meas. Sci. Technol. 22, 105803.
296. Kwon O, Lee JY and Yoon JR 2002a Equipotential line method for magnetic resonance electrical impedance tomography (MREIT). Inv. Prob. 18, 1089-1100.
297. Kwon O, Woo EJ, Yoon JR and Seo JK 2002b Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm. IEEE Trans. Biomed. Eng. 48, 160-167.
298. Kwon O, Park C, Park EJ, Seo JK and Woo EJ 2005 Electrical conductivity imaging using a variational method in Bz-based MREIT. Inv. Prob. 21, 969-980.
299. Kwon O, Pyo H, Seo JK and Woo EJ 2006 Mathematical framework for Bz-based MREIT model in electrical impedance imaging. Int. J. Comput. Math. Appl. 51, 817-828.
300. Kwon OI, Lee BI, Nam HS and Park C 2007 Noise analysis and MR pulse sequence optimization in MREIT using an injected current nonlinear encoding (ICNE) method. Physiol. Meas. 28, 1391-1404.
301. Lee BI, Oh SH, Woo EJ, Lee SY, Cho MH, Kwon O, Seo JK and Baek WS 2003a Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT). Physiol. Meas. 24, 579-589.
302. Lee BI, Lee SH, Kim TS, Kwon O, Woo EJ and Seo JK 2005 Harmonic decomposition in PDE-based denoising technique for magnetic resonance electrical impedance tomography. IEEE Trans. Biomed. Eng. 52, 1912-1920.
303. Lee BI, Park C, Pyo HC, Kwon O and Woo EJ 2006 Optimization of current injection pulse width in MREIT. Physiol. Meas. 28, N1-7.
304. Liu JJ, Seo JK, Sini M and Woo EJ 2007 On the convergence of the harmonic Bz algorithm in magnetic resonance electrical impedance tomography. SIAM J. Appl. Math. 67, 1259-1282.
305. Minhas AS, Kim HJ, Kim YT, Jeong WC, Woo EJ and Seo JK 2008 Conductivity imaging of postmortem swine leg using MREIT. In Proc. 9th Int Conf. on Electrical Impedance Tomography, Dartmouth, NH.
306. Minhas AS, Woo EJ and Lee SY 2009 Magnetic flux density measurement with balanced steady state free precession pulse sequence for MREIT: a simulation study. In Conf. Proc. IEEE Engineering in Medicine and Biology Society, Minneapolis, MN, pp. 2276-2278.
307. Muftuler LT, Hamamura MJ, Birgul O and Nalcioglu O 2004 Resolution and contrast in magnetic resonance electrical impedance tomography (MREIT) and its application to cancer imaging. Technol. Cancer Res. Treat. 3, 599-609.
308. Muftuler LT, Hamamura MJ, Birgul O and Nalcioglu O 2006 In vivo MRI electrical impedance tomography (MREIT) of tumors. Technol. Cancer Res. Treat. 5, 381-387.
309. Nachman A, Tamasan A and Timonov A 2007 Conductivity imaging with a single measurement of boundary and interior data. Inv. Prob. 23, 2551-2563.
310. Nachman A, Tamasan A and Timonov A 2009 Recovering the conductivity from a single measurement of interior data. Inv. Prob. 25, 035014.
311. Nam HS and Kwon OI 2010 Optimization of multiply acquired magnetic flux density B(z) using ICNEmultiecho train in MREIT. Phys. Med. Biol. 55, 2743-2759.
312. Oh SH, Lee BI, Woo EJ, Lee SY, Cho MH, Kwon O and Seo JK 2003 Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography. Phys. Med. Biol. 48, 3101-3116.
313. Oh SH, Lee BI, Park TS, Lee SY, Woo EJ, Cho MH, Kwon O and Seo JK 2004 Magnetic resonance electrical impedance tomography at 3 Tesla field strength. Magn. Reson. Med. 51, 1292-1296.
314. Oh SH, Lee BI, Woo EJ, Lee SY, Kim TS, Kwon O and Seo JK 2005 Electrical conductivity images of biological tissue phantoms in MREIT. Physiol. Meas. 26, S279-288.
315. Oh TI, Cho Y, Hwang YK, Oh SH, Woo EJ and Lee SY 2006 Improved current source design to measure induced magnetic flux density distributions in MREIT. J. Biomed. Eng. Res. 27, 30-37.
316. Park C, Kwon O, Woo EJ and Seo JK 2004a Electrical conductivity imaging using gradient Bz decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT). IEEE Trans. Med. Imag. 23, 388-394.
317. Park C, Park EJ, Woo EJ, Kwon O and Seo JK 2004b Static conductivity imaging using variational gradient Bz algorithm in magnetic resonance electrical impedance tomography. Physiol. Meas. 25, 275-269.
318. Park C, Lee BI, Kwon O and Woo EJ 2006 Measurement of induced magnetic flux density using injection current nonlinear encoding (ICNE) in MREIT. Physiol. Meas. 28, 117-127.
319. Reilly JP 1998 Applied Bioelectricity: From Electrical Stimulation to Electropathology. Springer, New York.
320. Sadleir R 2005 Noise analysis in MREIT at 3 and 11 Tesla field strength. Physiol. Meas. 26, 875-884.
321. Scott GC, Joy MLG, Armstrong RL and Henkelman RM 1991 Measurement of nonuniform current density by magnetic resonance. IEEE Trans. Med. Imag. 10, 362-374.
322. Scott GC, Joy MLG, Armstrong RL and Hankelman RM 1992 Sensitivity of magnetic resonance current density imaging. J. Magn. Reson. 97, 235-254.
323. Seo JK 1996 A uniqueness result on inverse conductivity problem with two measurements. J. Fourier Anal. Appl. 2, 515-524.
324. Seo JK and Woo EJ 2011 Magnetic resonance electrical impedance tomography (MREIT). SIAM Rev. 53, 40-68.
325. Seo JK, Kwon O, Lee BI and Woo EJ 2003a Reconstruction of current density distributions in axially symmetric cylindrical sections using one component of magnetic flux density: computer simulation study. Physiol. Meas. 24, 565-577.
326. Seo J K, Yoon J R, Woo E J and Kwon O 2003b Reconstruction of conductivity and current density images using only one component of magnetic field measurements. IEEE Trans. Biomed. Eng. 50, 1121-1124.
327. Seo JK, Pyo HC, Park CJ, Kwon O and Woo EJ 2004 Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study. Phys. Med. Biol. 49, 4371-4382.
328. Seo JK, Kim SW, Kim S, Liu J, Woo EJ, Jeon K and Lee CO 2008 Local harmonic Bz algorithm with domain decomposition in MREIT: computer simulation study. IEEE Trans. Med. Imag. 27, 1754-1761. Verchota G 1984 Layer potentials and boundary value problems for Laplace equation in Lipschitz domains. J. Funct. Anal. 59, 572-611.
329. Woo EJ and Seo JK 2008 Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging. Physiol. Meas. 29, R1-26.
330. Woo EJ, Lee SY and Mun CW 1994 Impedance tomography using internal current density distribution measured by nuclear magnetic resonance. Proc. SPIE 2299, 377-385.
331. Zhang N 1992 Electrical impedance tomography based on current density imaging. MS Thesis, University of Toronto, Canada.
332. Chaudhry H, Bukiet B and Findley T 2008 Mathematical analysis of applied loads on skeletal muscles during manual therapy. J. Am. Osteopath Assoc. 108, 680-688.
333. Doyley MM 2012 Topical review: Model-based elastography: a survey of approaches to the inverse elasticity problem. Phys. Med. Biol. 57, R35.
334. Dresner MA, Rose GH, Rossman PJ, Muthupillai R, Manduca A and Ehman RL 2001 Magnetic resonance elastography of skeletal muscle. J. Magn. Reson. Imag. 13, 269-276.
335. Gao L, Parker KJ, Lerner RM and Levinson SF 1996 Imaging of the elastic properties of tissue - a review. Ultrasound Med. Biol. 22, 959-977.
336. Gennisson JL, Catheline S, Chaffai S and Fink M 2003 Transient elastography in anisotropic medium: application to the measurement of slow and fast shear wave speeds in muscles. J. Acoust. Soc. Am. 114, 536-541.
337. Heers G, Jenkyn T, Dresner MA, Klein MO, Basford JR, Kaufman KR, Ehman RL and An KN 2003 Measurement of muscle activity with magnetic resonance elastography. Clin. Biomech. 18, 537-542.
338. Humphrey JD 2003 Continuum biomechanics of soft biological tissues. Proc. R. Soc. Lond. A 459, 3-46.
339. Kruse SA, Smith JA, Lawrence AJ, Dresner MA, Manduca A, Greenleaf JF and Ehman RL 2000 Tissue characterization using magnetic resonance elastography: preliminary results. Phys. Med. Biol. 45, 1579-1590.
340. Kwon OI, Park C, Nam HS, Woo EJ, Seo JK, Glaser KJ, Manduca A and Ehman RL 2009 Shear modulus decomposition algorithm in magnetic resonance elastography. IEEE Trans. Med. Imag. 28, 1526-1533.
341. Landau LD and Lifshitz EM 1986 Theory of Elasticity, 3rd edn. Pergamon Press, Oxford.
342. Lee TH, Ahn CY, Kwon OI and Seo JK 2010 A hybrid one-step inversion method for shear modulus imaging using time-harmonic vibrations. Inv. Prob. 26, 085014.
343. Lerner RM and Parker KJ 1987 Sono-elasticity in ultrasonic tissue characterization and echographic imaging. In Proc. 7th European Communities Workshop, Nijmegen, The Netherlands, ed. J Thijssen. European Communities, Luxembourg.
344. Low RN, Bonekamp S, Motosugi U, Lee JM, Reeder S, Bensamoun SF and Charleux F 2010 MRE in Clinical Practice: Case Review Compendium. A GE Healthcare MR publication.
345. Manduca A, Oliphant TE, Dresner MA, Mahowald JL, Kruse SA, Amromin E, Felmlee JP, Greenleaf JF and Ehman RL 2001 Magnetic resonance elastography: non-invasive mapping of tissue elasticity. Med. Image Anal. 5, 237-254.
346. Manduca A, Oliphant TE, Lake DS, Dresner MA and Ehman RL 2002 Characterization and evaluation of inversion algorithms for MR elastography. Proc. SPIE 4684, 1180-1185.
347. Manduca A, Lake DS and Ehman RL 2003 Spatio-temporal directional filtering for improved inversion of MR elastography images. Med. Image Anal. 7, 465-473.
348. Mariappan YK, Glaser KJ and Ehman RL 2010 Magnetic resonance elastography: a review. Clin. Anat., 23, 497-511.
349. McLaughlin JR and Renzi D 2006 Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts. Inv. Prob. 22, 681-706.
350. McLaughlin JR and Yoon JR 2004 Unique identifiability of elastic parameters from time dependent interior displacement measurement. Inv. Prob. 20, 25-45.
351. McLaughlin JR, Renzi D and Yoon JR 2007 Anisotropy reconstruction from wave fronts in transversely isotropic acoustic media. SIAM J. Appl. Math 68, 24-42.
352. Muthupillai R, Lomas DJ, Rossman PJ, Greenleaf JF, Manduca A and Ehman RL 1995 Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 269, 1854-1857.
353. Oliphant TE, Manduca A, Greenleaf JF and Ehman RL 2000a Direct, fast estimation of complex-valued stiffness for magnetic resonance elastography. International Society for Magnetic Resonance in Medicine, Berkeley, CA.
354. Oliphant TE, Kinnick RR, Manduca A, Ehman RL and Greenleaf JF 2000b An error analysis of Helmholtz inversion for incompressible shear, vibration elastography with application to filter design for tissue characterization. In Proc. IEEE Ultrasonics Symp., vol. 2, pp. 1795-1798. IEEE, New York.
355. Oliphant TE, Manduca A, Ehman RL and Greenleaf JF 2001 Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation. Magn. Reson. Med. 45, 299-310.
356. Ophir J, Cespedes I, Ponnekanti H, Yazdi Y and Li X 1991 Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason. Imag. 13, 111-134.
357. Papazoglou S, Braun J, Hamhaber U and Sack I 2005 Two-dimensional waveform analysis in MR elastography of skeletal muscles. Phys. Med. Biol. 50, 1313-1325.
358. Pujol J 2002 Elastic Wave Propagation and Generation in Seismology. Cambridge University Press, Cambridge.
359. Richter GR 1981 An inverse problem for the steady state diffusion equation. SIAM J. Appl. Math. 41, 210-221.
360. Sack I, Bernarding J and Braun J 2002 Analysis of wave patterns in MR elastography of skeletal muscle using coupled harmonic oscillator simulations. Magn. Reson. Imag. 20, 95-104.
361. Sinkus R, Lorenzen J, Schrader D, Lorenzen M, Dargatz M and Holz D 2000 High-resolution tensor MR elastography for breast tumour detection. Phys. Med. Biol. 45, 1649-1664.
362. Sinkus R, Tanter M, Catheline S, Lorenzen J, Kuhl C, Sondermann E and Fink M 2005a Imaging anisotropic and viscous properties of breast tissue by magnetic resonance elastography. Magn. Reson. Med. 53, 372-387.
363. Sinkus R, Tanter M, Xydeas T, Catheline S, Bercoff J and Fink M 2005b Viscoelastic shear properties of in vivo breast lesions measured by MR elastography. J. Magn. Reson. Imag. 23, 159-165.
364. Venkatesh SK, Yin M, Glockner JF, Takahashi N, Araoz PA, Talwalkar JA and Ehman RL 2008 MR elastography of liver tumors: preliminary results. Am. J. Roent. 190, 1534-1540.
365. Uffmann K, Maderwald S, Ajaj W, Galban CG, Mateiescu S, Quick HH and Ladd ME 2004 In vivo elasticity measurements of extremity skeletal muscle with MR elastography. NMR Biomed., 17, 181-190.
366. Yin M, Talwalkar JA, Glaser KJ, Manduca A, Grimm RC, Rossman PJ, Fidler JL and Ehman RL 2007 Assessment of hepatic fibrosis with magnetic resonance elastography. Clin. Gastroenterol. Hepatol. 5, 1207-1213.