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Newton method to recover the phase accumulated during MRI data acquisition. (English) Zbl 1264.92031
Summary: For an internal conductivity image, magnetic resonance electrical impedance tomography (MREIT) injects an electric current into an object and measures the induced magnetic flux density, which appears in the phase part of the acquired MR image data. To maximize signal intensity, the injected current nonlinear encoding (ICNE) method extends the duration of the current injection until the end of the MR data reading. It disturbs the usual linear encoding of the MR k-space data used in the inverse Fourier transform. In this study, we estimate the magnetic flux density, which is recoverable from nonlinearly encoded MR k-space data by applying a Newton method.
92C55 Biomedical imaging and signal processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Full Text: DOI
[1] M. Joy, G. Scott, and M. Henkelman, “In vivo detection of applied electric currents by magnetic resonance imaging,” Magnetic Resonance Imaging, vol. 7, no. 1, pp. 89-94, 1989.
[2] M. Eyuboglu, O. Birgul, and Y. Z. Ider, “A dual modality system for high resolution.true conductivity imaging,” in Proceedings of the 11th International Conference on Electrical Bioimpedance (ICEBI ’01), pp. 409-413, 2001.
[3] Y. Z. Ider and O. Birgul, “Use of the magnetic field generated by the internal distri- bution of injected currents for Electrical Impedance Tomography (MR-EIT),” Elektrik, vol. 6, pp. 215-225, 1998.
[4] H. S. Khang, B. I. Lee, S. H. Oh et al., “J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images,” IEEE Transactions on Medical Imaging, vol. 21, no. 6, pp. 695-702, 2002. · doi:10.1109/TMI.2002.800604
[5] B. I. Lee, S. H. Oh, E. J. Woo et al., “Three-dimensional forward solver and its performance analysis for magnetic resonance electrical impedance tomography (MREIT) using recessed electrodes,” Physics in Medicine and Biology, vol. 48, no. 13, pp. 1971-1986, 2003. · doi:10.1088/0031-9155/48/13/309
[6] S. H. Oh, B. I. Lee, E. J. Woo et al., “Electrical conductivity images of biological tissue phantoms in MREIT,” Physiological Measurement, vol. 26, no. 2, pp. S279-S288, 2005. · doi:10.1088/0967-3334/26/2/026
[7] R. Sadleir, S. Grant, S. U. Zhang, S. H. Oh, B. I. Lee, and E. J. Woo, “High field MREIT: setup and tissue phantom imaging at 11 T,” Physiological Measurement, vol. 27, no. 5, pp. S261-S270, 2006. · doi:10.1088/0967-3334/27/5/S22
[8] G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Measurement of nonuniform current density by magnetic resonance,” IEEE Transactions on Medical Imaging, vol. 10, no. 3, pp. 362-374, 1991. · doi:10.1109/42.97586
[9] J. K. Seo, J. R. Yoon, E. J. Woo, and O. Kwon, “Reconstruction of conductivity and current density images using only one component of magnetic field measurements,” IEEE Transactions on Biomedical Engineering, vol. 50, no. 9, pp. 1121-1124, 2003. · doi:10.1109/TBME.2003.816080
[10] E. J. Woo, J. K. Seo, and S. Y. Lee, “Magnetic resonance electrical impedance tomography (MREIT),” in Electrical Impedance Tomography: Methods, History and Applications, D. Holder, Ed., IOP Publishing, Bristol, UK, 2005. · Zbl 1210.35293
[11] M. L. Joy, “MR current density and conductivity imaging: the state of the art,” in Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC ’04), pp. 5315-5319, San Francisco, Calif, USA, 2004.
[12] G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Sensitivity of magnetic-resonance current-density imaging,” Journal of Magnetic Resonance, vol. 97, no. 2, pp. 235-254, 1992.
[13] N. Zhang, Electrical impedance tomography based on current density imaging [M.S. thesis], Department of Electrical Engineering, University of Toronto, Toronto, Canada, 1992.
[14] O. I. Kwon, B. I. Lee, H. S. Nam, and C. Park, “Noise analysis and MR pulse sequence optimization in MREIT using an injected current nonlinear encoding (ICNE) method,” Physiological Measurement, vol. 28, no. 11, pp. 1391-1404, 2007. · doi:10.1088/0967-3334/28/11/006
[15] C. Park, B. I. Lee, O. Kwon, and E. J. Woo, “Measurement of induced magnetic flux density using injection current nonlinear encoding (ICNE) in MREIT,” Physiological Measurement, vol. 28, no. 2, pp. 117-127, 2007. · doi:10.1088/0967-3334/28/2/001
[16] E. M. Haacke, R. W. Brown, M. R. Thompson, and R. Venkatesan, Magnetic Resonance Imaging: Physical Principles and Sequence Design, John Wiley & Sons, New York, NY, USA, 1999.
[17] R. Kress, Numerical Analysis, vol. 181 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. · Zbl 0913.65001 · doi:10.1007/978-1-4612-0599-9
[18] W. Gautschi, “On inverses of Vandermonde and confluent Vandermonde matrices,” Numerische Mathematik, vol. 4, pp. 117-123, 1962. · Zbl 0108.12501 · doi:10.1007/BF01386302 · eudml:131521
[19] W. Gautschi, “Norm estimates for inverses of Vandermonde matrices,” Numerische Mathematik, vol. 23, pp. 337-347, 1975. · Zbl 0304.65031 · doi:10.1007/BF01438260 · eudml:132312
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