A Novel Hopfield Neural Network for Perfect Calculation of Magnetic Resonance Spectroscopy
In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)" that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.
[1] Ala-Korpela, M., Changani, K.K., Hiltunen, Y., Bell, J.D., Fuller, B.J.,
Bryant, D.J., Taylor-Robinson, S.D. and Davidson, B.R. , "Assessment
of quantitative artificial neural network analysis in a metabolically
dynamic ex vivo 31P NMR pig liver study," Magnetic Resonace in
Medicine, vol. 38, 1997, pp. 840-844.
[2] Belliveau, J.W., Kennedy Jr, D.N., McKinstry, R.C., Buchbinder, B.R.,
Weisskoff, R.M., Cohen, M.S., Vevea, J.M., Brandy, T.J. and Rosen,
B.R., "Functional mapping of the human visual cortex by magnetic
resonance imaging," Science, vol. 254, no.5032, 1991, pp.716-719.
[3] Benvenuto, N. and Piazza, F., "On the complex backpropagation
algorithm. Institute of Electrical and Electronic Engineers," IEEE
Transaction on Signal Processing, vol. 40, no. 4, 1992., pp. 967-969.
[4] Cooley, J.W. and Tukey, J.W. "An algorithm for machine calculation of
complex Fourier series," Mathematics and Computation, vol. 19 , no.
90, 1965, pp. 297-301.
[5] David, H.A., Hinton, G.E. and Sejnowski, T.J., "A Learning Algorithm
for Boltzmann Machines," Cognitive Science: A Multidisciplinary
Journal, vol. 9, no. 1, 1985, pp. 149-169.
[6] Dayhoff, J.E., Neural Network Architectures: An Introduction. New
York, USA: Van Nostrand Reinhold, 1989.
[7] Derome, A.E.. Modern NMR Techniques for Chemistry Research
(Organic Chemistry Series, Vol 6), Oxford, United Kingdom: Pergamon
Press, 1987.
[8] El-Bakry, H..M., "New Fast Time Delay Neural Networks Using Cross
Correlation Performed in the Frequency Domain," Neurocomputing
Journal, vol. 69, 2006, pp. 2360-2363.
[9] El-Bakry, H.M. and Zhao, Q., "Fast Time Delay Neural Networks,"
International Journal of Neural Systems, vol. 15, no. 6, 2005, pp. 445-
455.
[10] Feinberg, D.A. and Oshio, K., "GRASE (gradient and spin echo) MR
imaging: A new fast clinical imaging technique," Radiology, vol. 181,
pp. 597-602.
[11] Geman, S. and Geman, D., "Stochastic Relaxation, Gibbs Distribution
and the Bayesian Restoration of Images," IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 6, 1984, pp. 721-741.
[12] Georgiou, G. M. and Koutsougeras, C. , "Complex domain
backpropagation," IEEE Transactions on Circuits and System," Analog
and Digital Signal Processing, vol. 39 no. 5, 1992, pp. 330-334.
[13] Han, L. and Biswas, S.K., "Neural networks for sinusoidal frequency
estimation," Journal of The Franklin Institute, vol. 334B, no. 1, 1997,
pp. 1-18.
[14] Haselgrove, J.C., Subramanian, V.H., Christen, R. and Leigh, J.S.,
"Analysis of in-vivo NMR spectra," Reviews of Magnetic Resonance in
Medicine, vol. 2, 1988, pp. 167-222.
[15] Henning, J., Nauerth, A. and Fnedburg, H., "RARE imaging: A first
imaging method for clinical MR," Magnetic Resonance in Medicine, vol.
3, no. 6, 1986, pp. 823-833.
[16] Hinton, G.E. and Sejnowski, T.J., "Learning and Relearning in
Boltzmann Machine," Parallel distributed processing: explorations in
the microstructure of cognition, vol. 1: foundations (pp. 282-317).
Cambridge, MA, USA: MIT press, 1986.
[17] Hirose, A., "Dynamics of fully complex-valued neural networks,"
Electrronics Letters, vol. 28, no. 16, 1992a, pp. 1492-1494.
[18] Hirose, A., "Proposal of fully complex-valued neural networks,"
Proceedings of International Joint Conference on Neural Networks: Vol.
4, 1992b, pp. 152-157, Baltimore, MD, USA.
[19] Hopfield, J.J., "Neural networks and physical systems with emergent
collective computational abilities," Proceeding of National Academic of
Science in USA: Vol. 79, 1982, pp. 2554-2558.
[20] Hopfield, J.J., "Neurons with graded response have collective
computational properties like those of two-state neurons," Proceeding of
National Academic of Science in USA, Vol. 81, 1984, pp. 3088-3092.
[21] Jankowski, S., Lozowski, A. and Zurada, J.M., "Complex-valued
multistate neural associative memory," Proceedings of IEEE
Transactions on Neural Networks, vol. 7, no. 6, 1996, pp. 1491-1496.
[22] Kaartinen, J., Mierisova, S., Oja, J.M.E., Usenius, J.P., Kauppinen, R.A.
and Hiltunen, Y., "Automated quantification of human brain metabolites
by artificial neural network analysis from in vivo single-voxel 1H NMR
spectra," Journal of Magnetic Resonance, vol. 134, 1998, pp. 176-179.
[23] Kuroe, Y., Hashimoto. N. and Mori, T., " On energy function for
complex-valued neural networks and its applications," Neural
information proceeding, Proceedings of the 9th International Conference
on Neural Information Processing. Computational Intelligence for the
E-Age. Vol.3, 2002, pp. 1079-1083.
[24] Kwong, K., Belliveau, J.W., Chesler, D.A., Goldberg, I.E., Weisskoff,
R.M., Poncelet, B.P., Kennedy, D.N., Hoppel, B.E., Cohen, M.S.,
Turner, R., Cheng, H., Brady, T.J. and Rosen, B.R., "Dynamic magnetic
resonance imaging of human brain activity during primary sensory
stimulation," Proceedings of the National Academy of Sciences, vol 89,
no. 12, 1992, pp. 5675-5679.
[25] Maddams, W.F., "The scope and Limitations of Curve Fitting," Applied
Spectroscopy, vol. 34, no. 3, 1980, pp. 245-267.
[26] Mansfield, P., "Multi-planar image formation using NMR spin echoes,"
Journal of Physical C: Solid State Physics, vol. 10, 1977, pp. 55-58.
[27] Melki, P.S., Mulkern, R.V., Panych, L.S. and Jolesz, F.A. , "Comparing
the FAISE method with conventional dual-echo sequences," Journal of
Magnetic Resonance Imaging, vol. 1, 1991, pp. 319-326.
[28] Meyer, C.H., Hu, B.S., Nishimura, D.G. and Macovski, A. , "Fast Spiral
Coronary Artery Imaging," Magnetic Resonance in Medicine, vol. 28,
no. 2, 1992, pp. 202-213.
[29] Miersová, S. and Ala-Korpela, M., "MR spectroscopy quantification: a
review of frequency domain methods," NMR in Biomedicine, vol.14,
2001, pp.247-259.
[30] Morita, N. and Konishi, O., "A Method of Estimation of Magnetic
Resonance Spectroscopy Using Complex-Valued Neural Networks,"
Systems and Computers in Japan, vol. 35, no. 10, 2004, pp. 14-22.
[31] Naressi, A., Couturier, C., Castang, I., de. Beer, R. and Graveron-
Demilly, D., "Java-based graphical user interface for MRUI, a software
package for quantitation of in vivo medical magnetic resonance
spectroscopy signals," Computers in Biology and Medicine, vol.31,
2001, pp. 269-286.
[32] Nitta, T., "An Extension of the Back-Propagation Algorithm to Complex
Numbers," Neural Networks, vol. 10, no. 8, 1997, pp. 1392-1415.
[33] Nitta, T., "An Analysis of the Fundamental Structure of Complex-
Valued Neurons," Neural Processing Letters, vol. 12, no. 3, 2000, pp.
239-246.
[34] Nitta, T., "Redundancy of the Parameters of the Complex-valued Neural
Networks. Neurocomputing," vol. 49, no. (1-4), 2002, pp. 423-428.
[35] Nitta, T., "On the Inherent Property of the Decision Boundary in
Complex-valued Neural Networks," Neurocomputing, vol. 50(c), 2003,
pp. 291-303.
[36] Nitta, T., "Solving the XOR Problem and the Detection of Symmetry
Using a Single Complex-valued Neuron," Neural Networks, vol. 16, no.
8, 2003, pp. 1101-1105.
[37] Nitta, T., "The Uniqueness Theorem for Complex-valued Neural
Networks and the Redundancy of the Parameters," Systems and
Computers in Japan, vol. 34, no.14, 2003, pp. 54-62.
[38] Nitta, T., " Orthogonality of Decision Boundaries in Complex-Valued
Neural Networks," Neural Computation, vol. 16, no.1, 2003, pp73-97.
[39] Nitta, T., " Reducibility of the Complex-valued Neural Network,"
Neural Information Processing - Letters and Reviews, vol. 2, no. 3,
2004, pp. 53-56.
[40] Ogawa, S., Lee, T.M., Nayak, A.S. and Glynn, P., "Oxygenationsensitive
contrast in magnetic resonance image of rodent brain at high
magnetic fields," Magnetic Resonance in Medicine, vol. 14, no. 1, 1990,
pp. 68-78.
[41] Provencher, S., W., " Automatic quantification of localized in vivo 1H
spectra with LCModel," NMR in Biomedicine, vol. 14 no. 4, 2001, pp.
260-264.
[42] Rumelhart, D,E, Hinton, G.E. and Williams, R.J., Learning internal
representations by error propagation, In Rumelhart, D,E and
McClelland, J.L.(Eds.), Parallel Distributed Processing: Volume
1:Foundations (pp.318-362), Cambridge, MA, USA: MIT press, 1986.
[43] van den Boogaart, A., Van Hecke, P., Van Hulfel, S., Graveron-
Dermilly, D., van Ormondt, D. and de Beer, R., "MRUI: a graphical user
interface for accurate routine MRS data analysis," Proceeding of the
European Society for Magnetic Resonance in Medicine and Biology 13th
Annual Meeting, Prague, (p.318), 1996.
[44] van Huffel, S., Chen, H., Decanniere, C. and Hecke, P.V. , "Algorithm
for time-domain NMR data fitting based on total least squares.,"
Journal of Magnetic Resonance A, vol. 110, pp. 228-237.
[45] Sijens, P.E., Dagnelie, P.C., Halfwrk, S., van Dijk, P., Wicklow, K. and
Oudkerk, M., "Understanding the discrepancies between 31P MR
spectroscopy assessed liver metabolite concentrations from different
institutions," Magnetic Resonance Imaging, vol. 16, no. 2, 1998, pp.
205-211.
[46] Zhou, C. and Liu, L., "Complex Hopfield model," Optics
Communications, vol. 103, no. 1-2, 1993, pp. 29-32.
[1] Ala-Korpela, M., Changani, K.K., Hiltunen, Y., Bell, J.D., Fuller, B.J.,
Bryant, D.J., Taylor-Robinson, S.D. and Davidson, B.R. , "Assessment
of quantitative artificial neural network analysis in a metabolically
dynamic ex vivo 31P NMR pig liver study," Magnetic Resonace in
Medicine, vol. 38, 1997, pp. 840-844.
[2] Belliveau, J.W., Kennedy Jr, D.N., McKinstry, R.C., Buchbinder, B.R.,
Weisskoff, R.M., Cohen, M.S., Vevea, J.M., Brandy, T.J. and Rosen,
B.R., "Functional mapping of the human visual cortex by magnetic
resonance imaging," Science, vol. 254, no.5032, 1991, pp.716-719.
[3] Benvenuto, N. and Piazza, F., "On the complex backpropagation
algorithm. Institute of Electrical and Electronic Engineers," IEEE
Transaction on Signal Processing, vol. 40, no. 4, 1992., pp. 967-969.
[4] Cooley, J.W. and Tukey, J.W. "An algorithm for machine calculation of
complex Fourier series," Mathematics and Computation, vol. 19 , no.
90, 1965, pp. 297-301.
[5] David, H.A., Hinton, G.E. and Sejnowski, T.J., "A Learning Algorithm
for Boltzmann Machines," Cognitive Science: A Multidisciplinary
Journal, vol. 9, no. 1, 1985, pp. 149-169.
[6] Dayhoff, J.E., Neural Network Architectures: An Introduction. New
York, USA: Van Nostrand Reinhold, 1989.
[7] Derome, A.E.. Modern NMR Techniques for Chemistry Research
(Organic Chemistry Series, Vol 6), Oxford, United Kingdom: Pergamon
Press, 1987.
[8] El-Bakry, H..M., "New Fast Time Delay Neural Networks Using Cross
Correlation Performed in the Frequency Domain," Neurocomputing
Journal, vol. 69, 2006, pp. 2360-2363.
[9] El-Bakry, H.M. and Zhao, Q., "Fast Time Delay Neural Networks,"
International Journal of Neural Systems, vol. 15, no. 6, 2005, pp. 445-
455.
[10] Feinberg, D.A. and Oshio, K., "GRASE (gradient and spin echo) MR
imaging: A new fast clinical imaging technique," Radiology, vol. 181,
pp. 597-602.
[11] Geman, S. and Geman, D., "Stochastic Relaxation, Gibbs Distribution
and the Bayesian Restoration of Images," IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 6, 1984, pp. 721-741.
[12] Georgiou, G. M. and Koutsougeras, C. , "Complex domain
backpropagation," IEEE Transactions on Circuits and System," Analog
and Digital Signal Processing, vol. 39 no. 5, 1992, pp. 330-334.
[13] Han, L. and Biswas, S.K., "Neural networks for sinusoidal frequency
estimation," Journal of The Franklin Institute, vol. 334B, no. 1, 1997,
pp. 1-18.
[14] Haselgrove, J.C., Subramanian, V.H., Christen, R. and Leigh, J.S.,
"Analysis of in-vivo NMR spectra," Reviews of Magnetic Resonance in
Medicine, vol. 2, 1988, pp. 167-222.
[15] Henning, J., Nauerth, A. and Fnedburg, H., "RARE imaging: A first
imaging method for clinical MR," Magnetic Resonance in Medicine, vol.
3, no. 6, 1986, pp. 823-833.
[16] Hinton, G.E. and Sejnowski, T.J., "Learning and Relearning in
Boltzmann Machine," Parallel distributed processing: explorations in
the microstructure of cognition, vol. 1: foundations (pp. 282-317).
Cambridge, MA, USA: MIT press, 1986.
[17] Hirose, A., "Dynamics of fully complex-valued neural networks,"
Electrronics Letters, vol. 28, no. 16, 1992a, pp. 1492-1494.
[18] Hirose, A., "Proposal of fully complex-valued neural networks,"
Proceedings of International Joint Conference on Neural Networks: Vol.
4, 1992b, pp. 152-157, Baltimore, MD, USA.
[19] Hopfield, J.J., "Neural networks and physical systems with emergent
collective computational abilities," Proceeding of National Academic of
Science in USA: Vol. 79, 1982, pp. 2554-2558.
[20] Hopfield, J.J., "Neurons with graded response have collective
computational properties like those of two-state neurons," Proceeding of
National Academic of Science in USA, Vol. 81, 1984, pp. 3088-3092.
[21] Jankowski, S., Lozowski, A. and Zurada, J.M., "Complex-valued
multistate neural associative memory," Proceedings of IEEE
Transactions on Neural Networks, vol. 7, no. 6, 1996, pp. 1491-1496.
[22] Kaartinen, J., Mierisova, S., Oja, J.M.E., Usenius, J.P., Kauppinen, R.A.
and Hiltunen, Y., "Automated quantification of human brain metabolites
by artificial neural network analysis from in vivo single-voxel 1H NMR
spectra," Journal of Magnetic Resonance, vol. 134, 1998, pp. 176-179.
[23] Kuroe, Y., Hashimoto. N. and Mori, T., " On energy function for
complex-valued neural networks and its applications," Neural
information proceeding, Proceedings of the 9th International Conference
on Neural Information Processing. Computational Intelligence for the
E-Age. Vol.3, 2002, pp. 1079-1083.
[24] Kwong, K., Belliveau, J.W., Chesler, D.A., Goldberg, I.E., Weisskoff,
R.M., Poncelet, B.P., Kennedy, D.N., Hoppel, B.E., Cohen, M.S.,
Turner, R., Cheng, H., Brady, T.J. and Rosen, B.R., "Dynamic magnetic
resonance imaging of human brain activity during primary sensory
stimulation," Proceedings of the National Academy of Sciences, vol 89,
no. 12, 1992, pp. 5675-5679.
[25] Maddams, W.F., "The scope and Limitations of Curve Fitting," Applied
Spectroscopy, vol. 34, no. 3, 1980, pp. 245-267.
[26] Mansfield, P., "Multi-planar image formation using NMR spin echoes,"
Journal of Physical C: Solid State Physics, vol. 10, 1977, pp. 55-58.
[27] Melki, P.S., Mulkern, R.V., Panych, L.S. and Jolesz, F.A. , "Comparing
the FAISE method with conventional dual-echo sequences," Journal of
Magnetic Resonance Imaging, vol. 1, 1991, pp. 319-326.
[28] Meyer, C.H., Hu, B.S., Nishimura, D.G. and Macovski, A. , "Fast Spiral
Coronary Artery Imaging," Magnetic Resonance in Medicine, vol. 28,
no. 2, 1992, pp. 202-213.
[29] Miersová, S. and Ala-Korpela, M., "MR spectroscopy quantification: a
review of frequency domain methods," NMR in Biomedicine, vol.14,
2001, pp.247-259.
[30] Morita, N. and Konishi, O., "A Method of Estimation of Magnetic
Resonance Spectroscopy Using Complex-Valued Neural Networks,"
Systems and Computers in Japan, vol. 35, no. 10, 2004, pp. 14-22.
[31] Naressi, A., Couturier, C., Castang, I., de. Beer, R. and Graveron-
Demilly, D., "Java-based graphical user interface for MRUI, a software
package for quantitation of in vivo medical magnetic resonance
spectroscopy signals," Computers in Biology and Medicine, vol.31,
2001, pp. 269-286.
[32] Nitta, T., "An Extension of the Back-Propagation Algorithm to Complex
Numbers," Neural Networks, vol. 10, no. 8, 1997, pp. 1392-1415.
[33] Nitta, T., "An Analysis of the Fundamental Structure of Complex-
Valued Neurons," Neural Processing Letters, vol. 12, no. 3, 2000, pp.
239-246.
[34] Nitta, T., "Redundancy of the Parameters of the Complex-valued Neural
Networks. Neurocomputing," vol. 49, no. (1-4), 2002, pp. 423-428.
[35] Nitta, T., "On the Inherent Property of the Decision Boundary in
Complex-valued Neural Networks," Neurocomputing, vol. 50(c), 2003,
pp. 291-303.
[36] Nitta, T., "Solving the XOR Problem and the Detection of Symmetry
Using a Single Complex-valued Neuron," Neural Networks, vol. 16, no.
8, 2003, pp. 1101-1105.
[37] Nitta, T., "The Uniqueness Theorem for Complex-valued Neural
Networks and the Redundancy of the Parameters," Systems and
Computers in Japan, vol. 34, no.14, 2003, pp. 54-62.
[38] Nitta, T., " Orthogonality of Decision Boundaries in Complex-Valued
Neural Networks," Neural Computation, vol. 16, no.1, 2003, pp73-97.
[39] Nitta, T., " Reducibility of the Complex-valued Neural Network,"
Neural Information Processing - Letters and Reviews, vol. 2, no. 3,
2004, pp. 53-56.
[40] Ogawa, S., Lee, T.M., Nayak, A.S. and Glynn, P., "Oxygenationsensitive
contrast in magnetic resonance image of rodent brain at high
magnetic fields," Magnetic Resonance in Medicine, vol. 14, no. 1, 1990,
pp. 68-78.
[41] Provencher, S., W., " Automatic quantification of localized in vivo 1H
spectra with LCModel," NMR in Biomedicine, vol. 14 no. 4, 2001, pp.
260-264.
[42] Rumelhart, D,E, Hinton, G.E. and Williams, R.J., Learning internal
representations by error propagation, In Rumelhart, D,E and
McClelland, J.L.(Eds.), Parallel Distributed Processing: Volume
1:Foundations (pp.318-362), Cambridge, MA, USA: MIT press, 1986.
[43] van den Boogaart, A., Van Hecke, P., Van Hulfel, S., Graveron-
Dermilly, D., van Ormondt, D. and de Beer, R., "MRUI: a graphical user
interface for accurate routine MRS data analysis," Proceeding of the
European Society for Magnetic Resonance in Medicine and Biology 13th
Annual Meeting, Prague, (p.318), 1996.
[44] van Huffel, S., Chen, H., Decanniere, C. and Hecke, P.V. , "Algorithm
for time-domain NMR data fitting based on total least squares.,"
Journal of Magnetic Resonance A, vol. 110, pp. 228-237.
[45] Sijens, P.E., Dagnelie, P.C., Halfwrk, S., van Dijk, P., Wicklow, K. and
Oudkerk, M., "Understanding the discrepancies between 31P MR
spectroscopy assessed liver metabolite concentrations from different
institutions," Magnetic Resonance Imaging, vol. 16, no. 2, 1998, pp.
205-211.
[46] Zhou, C. and Liu, L., "Complex Hopfield model," Optics
Communications, vol. 103, no. 1-2, 1993, pp. 29-32.
@article{"International Journal of Information, Control and Computer Sciences:62808", author = "Hazem M. El-Bakry", title = "A Novel Hopfield Neural Network for Perfect Calculation of Magnetic Resonance Spectroscopy", abstract = "In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)" that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.
", keywords = "Hopfield Neural Networks, Cross Correlation, Nuclear Magnetic Resonance, Magnetic Resonance Spectroscopy, Fast Fourier Transform.", volume = "1", number = "5", pages = "1437-13", }
