Table of Contents Author Guidelines Submit a Manuscript
Computational Intelligence and Neuroscience
Volume 2010, Article ID 469658, 13 pages
http://dx.doi.org/10.1155/2010/469658
Research Article

Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits

Department of Electrical Engineering, Columbia University, New York, NY 10027, USA

Received 1 March 2009; Accepted 24 June 2009

Academic Editor: Zhe (Sage) Chen

Copyright © 2010 Aurel A. Lazar and Eftychios A. Pnevmatikakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. A. Lazar, “Time encoding with an integrate-and-fire neuron with a refractory period,” Neurocomputing, vol. 58–60, pp. 53–58, 2004. View at Publisher · View at Google Scholar
  2. A. A. Lazar and L. T. Tóth, “Perfect recovery and sensitivity analysis of time encoded bandlimited signals,” IEEE Transactions on Circuits and Systems I, vol. 51, no. 10, pp. 2060–2073, 2004. View at Publisher · View at Google Scholar
  3. O. Christensen, An Introduction to Frames and Riesz Bases, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 2003.
  4. G. Wahba, Spline Models for Observational Data, Society for Industrial Mathematics, 1990.
  5. A. A. Lazar and E. A. Pnevmatikakis, “Faithful representation of stimuli with a population of integrate-and-fire neurons,” Neural Computation, vol. 20, no. 11, pp. 2715–2744, 2008. View at Publisher · View at Google Scholar
  6. A. A. Lazar and E. A. Pnevmatikakis, “A video time encoding machine,” in Proceedings of the IEEE International Conference on Image Processing, San Diego, Calif, USA, October 2008.
  7. A. A. Lazar and E. A. Pnevmatikakis, “Reconstruction of sensory stimuli encoded with integrate-and-fire neurons with random thresholds,” EURASIP Journal on Advances in Signal Processing, vol. 2009, Article ID 682930, 14 pages, 2009. View at Publisher · View at Google Scholar
  8. G. L. Fain, Sensory Transduction, Sinauer Associates, Inc., 2003.
  9. D. Song, R. H. Chan, V. Z. Marmarelis, R. E. Hampson, S. A. Deadwyler, and T. W. Berger, “Nonlinear dynamic modeling of spike train transformations for hippocampal-cortical prostheses,” IEEE Transactions on Biomedical Engineering, vol. 54, no. 6, pp. 1053–1066, 2007. View at Publisher · View at Google Scholar
  10. T. P. Zanos, S. H. Courellis, T. W. Berger, R. E. Hampson, S. A. Deadwyler, and V. Z. Marmarelis, “Nonlinear modeling of causal interrelationships in neuronal ensembles,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 16, no. 4, pp. 336–352, 2008. View at Publisher · View at Google Scholar
  11. S.-P. Kim, J. C. Sanchez, Y. N. Rao et al., “A comparison of optimal MIMO linear and nonlinear models for brain-machine interfaces,” Journal of Neural Engineering, vol. 3, no. 2, pp. 145–161, 2006. View at Publisher · View at Google Scholar
  12. R. Serrano-Gotarredona, T. Serrano-Gotarredona, A. Acosta-Jiménez et al., “On real-time AER 2-D convolutions hardware for neuromorphic spike-based cortical processing,” IEEE Transactions on Neural Networks, vol. 19, no. 7, pp. 1196–1219, 2008. View at Publisher · View at Google Scholar
  13. A. I. Bezhaev and V. A. Vasilenko, Variational Theory of Splines, Kluwer Academic/Plenum Publishers, New York, NY, USA, 2001.
  14. R. H. Bartels, J. C. Beatty, and B. A. Barsky, An Introduction to Splines for Use in Computer Graphics & Geometric Modeling, Morgan Kaufmann, San Francisco, Calif, USA, 1987.
  15. M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing—part I: theory,” IEEE Transactions on Signal Processing, vol. 41, no. 2, pp. 821–833, 1993. View at Publisher · View at Google Scholar
  16. A. A. Lazar and E. A. Pnevmatikakis, “Consistent recovery of stimuli encoded with a neural ensemble,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3497–3500, Taipei, Taiwan, April 2009.
  17. J. Kybic, T. Blu, and M. Unser, “Generalized sampling: a variational approach. I: theory,” IEEE Transactions on Signal Processing, vol. 50, no. 8, pp. 1965–1976, 2002. View at Publisher · View at Google Scholar
  18. R. H. Masland, “The fundamental plan of the retina,” Nature Neuroscience, vol. 4, no. 9, pp. 877–886, 2001. View at Publisher · View at Google Scholar
  19. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics, Kluwer Academic Publishers, Boston, Mass, USA, 2004.
  20. E. M. Izhikevich, “Resonate-and-fire neurons,” Neural Networks, vol. 14, no. 6-7, pp. 883–894, 2001. View at Publisher · View at Google Scholar
  21. Ş. Mihalaş and E. Niebur, “A generalized linear integrate-and-fire neural model produces diverse spiking behaviors,” Neural Computation, vol. 21, no. 3, pp. 704–718, 2009. View at Publisher · View at Google Scholar
  22. R. Jolivet, R. Kobayashi, A. Rauch, R. Naud, S. Shinomoto, and W. Gerstner, “A benchmark test for a quantitative assessment of simple neuron models,” Journal of Neuroscience Methods, vol. 169, no. 2, pp. 417–424, 2008. View at Publisher · View at Google Scholar
  23. P. C. Bressloff and J. G. Taylor, “Dynamics of compartmental model neurons,” Neural Networks, vol. 7, no. 6-7, pp. 1153–1165, 1994. View at Google Scholar
  24. J. Duchon, “Splines minimizing rotation-invariant semi-norms in sobolev spaces,” in Constructive Theory of Functions of Several Variables, W. Schempp and K. Zeller, Eds., Springer, New York, NY, USA, 1977. View at Google Scholar