Citation: |
[1] |
G. Alessandrini, An identification problem for an elliptic equation in two variables, Ann. Mat. Pura Appl., 145 (1986), 265-295.doi: 10.1007/BF01790543. |
[2] |
H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink, Electrical impedance tomography by elastic deformation, SIAM J. Appl. Math., 68 (2008), 1557-1573.doi: 10.1137/070686408. |
[3] |
L. C. Evans and M. Gariepy, "Measure Theory and Fine Properties of Functions," CRC Press, Boca Raton, FL, 1992. |
[4] |
B. Gebauer and O. Scherzer, Impedance-acoustic tomography, SIAM J. Appl. Math., 69 (2008), 565-576.doi: 10.1137/080715123. |
[5] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. |
[6] |
E. Giusti, "Minimal Surfaces and Functions of Bounded Variation," Monographs in Mathematics 80, Birkhäuser Verlag, Basel, 1984. |
[7] |
M. L. Joy, A. Nachman, K. F. Hasanov, R. S. Yoon and A. W. Ma, A new approach to current density impedance imaging (CDII), Proceedings ISMRM, #2356 (Kyoto, Japan), 2004. |
[8] |
S. Kim, O. Kwon, J. K. Seo and J. R. Yoon, On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography, SIAM J. Math. Anal., 34 (2002), 511-526.doi: 10.1137/S0036141001391354. |
[9] |
O. Kwon, J. Y. Lee and and J. R. Yoon, Equipotential line method for magnetic resonance electrical impedance tomography, Inverse Problems, 18 (2002), 1089-1100.doi: 10.1088/0266-5611/18/4/310. |
[10] |
O. Kwon, E. J. Woo, J. R. Yoon and J. K. Seo, Magnetic resonance electric impedance tomography (MREIT): Simulation study of J-substitution algorithm, IEEE Trans. Biomed. Eng., 49 (2002), 160-167.doi: 10.1109/10.979355. |
[11] |
J. Y. Lee, A reconstruction formula and uniqueness of conductivity in MREIT using two internal current distributions, Inverse Problems, 20 (2004), 847-858.doi: 10.1088/0266-5611/20/3/012. |
[12] |
X. Li, Y. Xu and B. He, Imaging electrical impedance from acoustic measurements by means of magnetoacoustic tomography with magnetic Induction (MAT-MI), IEEE Transactions on Biomedical Engineering, 54 (2007), 323-330.doi: 10.1109/TBME.2006.883827. |
[13] |
A. Nachman, A. Tamasan and A. Timonov, Conductivity imaging with a single measurement of boundary and interior data, Inverse Problems, 23 (2007), 2551-2563.doi: 10.1088/0266-5611/23/6/017. |
[14] |
A. Nachman, A. Tamasan and A. Timonov, Recovering the conductivity from a single measurement of interior data, Inverse Problems, 25 (2009), 035014, 16pp. |
[15] |
A. Nachman, A. Tamasan and A. Timonov, Reconstruction of planar conductivities in subdomains from incomplete data, SIAM J. Appl. Math., 70 (2010), 3342-3362.doi: 10.1137/10079241X. |
[16] |
M. Z. Nashed and O. Scherzer, Stable approximation of nondifferentiable optimization problems with variational inequalities, Contemp. Math., 204 (1997), 155-170. |
[17] |
M. Z. Nashed and O. Scherzer, Stable approximation of a minimal surface problem with variational inequalitites, Abstr. and Appl. Anal., 2 (1997), 137-161.doi: 10.1155/S1085337597000316. |
[18] |
G. C. Scott, M. L. Joy, R. L. Armstrong and R. M. Henkelman, Measurement of nonuniform current density by magnetic resonance, IEEE Trans. Med. Imag., 10 (1991), 362-374.doi: 10.1109/42.97586. |
[19] |
N. Zhang, "Electrical Impedance Tomography Based on Current Density Imaging," M. Sc. Thesis, University of Toronto, Canada, 1992. |
[20] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. III. Variational Methods and Optimization," Springer-Verlag, New York, 1985. |
[21] |
W. P. Ziemer, "Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation," Springer-Verlag, New York, 1989. |