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2662 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007 analog input may not be accessible when no linear transducers are available for this. It will be the case, for instance, with sensory neurons, which form a thresholded all-or-nothing type of representation of an analog signal from the physical environment, bearing similarities with the representation by the present array of comparators [27], [29], [37]. This will also be the case with nanodevices with intrinsic nonlinearities and usable in building sensor microarrays [38]. The estimation aided by noise that we have described in arrays can be specially relevant in these contexts of intrinsically nonlinear sensing networks. This can provide a basis for devising novel unconventional intelligent sensing arrays that are capable of exploiting the noise. REFERENCES [1] O. Kanoun and H. R. Tränkler, “Sensor technology advances and future trends,” IEEE Trans. Instrum. Meas., vol. 53, no. 6, pp. 1497–1501, Dec. 2004. [2] J. S. Wilson, Sensor Technology Handbook. Boston, MA: Newnes, 2004. [3] M. D. McDonnell, D. Abbott, and C. E. M. Pearce, “An analysis of noise enhanced information transmission in an array of comparators,” Microelectron. J., vol. 33, no. 12, pp. 1079–1089, Dec. 2002. [4] M. A. Arbib, The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press, 2002. [5] L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Modern Phys., vol. 70, no. 1, pp. 223–287, Jan. 1998. [6] B. Andò, S. Baglio, S. Graziani, and N. Pitrone, “Optimal improvement in bistable measurement device performance via stochastic resonance,” Int. J. Electron., vol. 86, no. 7, pp. 791–806, Jul. 1999. [7] B. Andò and S. Graziani, Stochastic Resonance: Theory and Applications. Boston, MA: Kluwer, 2000. [8] B. Andò, S. Baglio, S. Graziani, and N. Pitrone, “Measurements of parameters influencing the optimal noise level in stochastic systems,” IEEE Trans. Instrum. Meas., vol. 49, no. 5, pp. 1137–1143, Oct. 2000. [9] B. Andò and S. Graziani, “Adding noise to improve measurement,” IEEE Instrum. Meas. Mag., vol. 4, no. 1, pp. 24–30, Mar. 2001. [10] G. P. Harmer, B. R. Davis, and D. Abbott, “A review of stochastic resonance: Circuits and measurement,” IEEE Trans. Instrum. Meas., vol. 51, no. 2, pp. 299–309, Apr. 2002. [11] A. Nikitin, N. G. Stocks, and A. R. Bulsara, “Signal detection via residence times statistics: Noise-mediated minimization of the measurement error,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 68, no. 3, pp. 036 133-1–036 133-4, Sep. 2003. [12] F. Chapeau-Blondeau and D. Rousseau, “Noise-enhanced performance for an optimal Bayesian estimator,” IEEE Trans. Signal Process., vol. 52, no. 5, pp. 1327–1334, May 2004. [13] S. Mitaim and B. Kosko, “Adaptive stochastic resonance,” Proc. IEEE, vol. 86, no. 11, pp. 2152–2183, Nov. 1998. [14] G. P. Harmer and D. Abbott, “Simulation of circuits demonstrating stochastic resonance,” Microelectron. J., vol. 31, no. 7, pp. 553–559, Jul. 2000. [15] J. J. Collins, C. C. Chow, and T. T. Imhoff, “Stochastic resonance without tuning,” Nature, vol. 376, no. 6537, pp. 236–238, Jul. 1995. [16] Z. Gingl, L. B. Kiss, and F. Moss, “Non-dynamical stochastic resonance: Theory and experiments with white and arbitrarily coloured noise,” Europhys. Lett., vol. 29, no. 3, pp. 191–196, Jan. 1995. [17] M. E. Inchiosa and A. R. Bulsara, “Signal detection statistics of stochastic resonators,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 53, no. 3, pp. R2 021–R2 024, Mar. 1996. [18] X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett., vol. 33, no. 20, pp. 1666–1668, Sep. 1997. [19] D. G. Luchinsky, R. Mannella, P. V. E. McClintock, and N. G. Stocks, “Stochastic resonance in electrical circuits—I: Conventional stochastic resonance,” IEEE Trans. Circuits Syst. II, vol. 46, no. 9, pp. 1205–1214, Sep. 1999. [20] F. Chapeau-Blondeau, “Noise-assisted propagation over a nonlinear line of threshold elements,” Electron. Lett., vol. 35, no. 13, pp. 1055–1056, Jun. 1999. [21] S. Zozor and P. O. Amblard, “On the use of stochastic resonance in sine detection,” Signal Process., vol. 82, no. 3, pp. 353–367, Mar. 2002. [22] N. G. Stocks, “Suprathreshold stochastic resonance in multilevel threshold systems,” Phys. Rev. Lett., vol. 84, no. 11, pp. 2310–2313, Mar. 2000. [23] N. G. Stocks, “Information transmission in parallel threshold arrays: Suprathreshold stochastic resonance,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 63, no. 4, pp. 041114-1–041114-9, Apr. 2001. [24] M. D. McDonnell, D. Abbott, and C. E. M. Pearce, “A characterization of suprathreshold stochastic resonance in an array of comparators by correlation coefficient,” Fluctuation Noise Lett., vol. 2, no. 3, pp. L205–L220, 2002. [25] D. Rousseau, F. Duan, and F. Chapeau-Blondeau, “Suprathreshold stochastic resonance and noise-enhanced Fisher information in arrays of threshold devices,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 68, no. 3, pp. 031107-1–031107-10, Sep. 2003. [26] D. Rousseau and F. Chapeau-Blondeau, “Suprathreshold stochastic resonance and signal-to-noise ratio improvement in arrays of comparators,” Phys. Lett. A, vol. 321, no. 5/6, pp. 280–290, Feb. 2004. [27] N. G. Stocks and R. Mannella, “Generic noise-enhanced coding in neuronal arrays,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 64, no. 3, pp. 030902-1–030902-4, Sep. 2001. [28] G. P. Harmer and D. Abbott, “Motion detection and stochastic resonance in noisy environments,” Microelectron. J., vol. 32, no. 12, pp. 959–967, Dec. 2001. [29] N. G. Stocks, D. Allingham, and R. P. Morse, “The application of suprathreshold stochastic resonance to cochlear implant coding,” Fluctuation Noise Lett., vol. 2, no. 3, pp. L169–L181, 2002. [30] D. Rousseau and F. Chapeau-Blondeau, “Constructive role of noise in signal detection from parallel arrays of quantizers,” Signal Process., vol. 85, no. 3, pp. 571–580, Mar. 2005. [31] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993. [32] S. Kay, “Can detectability be improved by adding noise?” IEEE Signal Process. Lett., vol. 7, no. 1, pp. 8–10, Jan. 2000. [33] F. Chapeau-Blondeau, “Stochastic resonance for an optimal detector with phase noise,” Signal Process., vol. 83, no. 3, pp. 665–670, Mar. 2003. [34] D. Rousseau and F. Chapeau-Blondeau, “Stochastic resonance and improvement by noise in optimal detection strategies,” Digit. Signal Process., vol. 15, no. 1, pp. 19–32, Jan. 2005. [35] F. Chapeau-Blondeau and D. Rousseau, “Constructive action of additive noise in optimal detection,” Int. J. Bifurc. Chaos, vol. 15, no. 9, pp. 2985– 2994, 2005. [36] R. M. Gray and D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2325–2383, 1998. [37] M. D. McDonnell and D. Abbott, “Open questions for suprathreshold stochastic resonance in sensory neural models for motion detection using artificial insect vision,” in Proc. AIP Conf., 2003, vol. 665, pp. L51–L58. [38] I. Y. Lee, X. Liu, B. Kosko, and C. Zhou, “Nanosignal processing: Stochastic resonance in carbon nanotubes that detect subthreshold signals,” Nano Lett., vol. 3, no. 12, pp. 1683–1686, 2003. David Rousseau was born in Le Mans, France, in 1973. He received the M.S. degree in acoustics and signal processing from the Institut de Recherche Coordination Acoustique et Musique, Paris, France, in 1996 and the Ph.D. degree in nonlinear signal processing from the Université d’Angers, Angers, France, in 2004. He is currently a Maître de Conférences with the Université d’Angers. François Chapeau-Blondeau was born in France in 1959. He received the Engineer Diploma from ESEO, Angers, France, in 1982, the Ph.D. degree in electrical engineering from University Paris 6, Paris, France, in 1987, and the Habilitation degree from the Université d’Angers in 1994. In 1988, he was a Research Associate with the Department of Biophysics, Mayo Clinic, Rochester, MN, working on biomedical ultrasonics. Since 1990, he has been with the Université d’Angers, where he is currently a Professor of electronic and information sciences. His research interests include nonlinear systems and signal processing, and the interface between physics and information sciences. 83/197
D. ROUSSEAU, G. V. ANAND, and F. CHAPEAU-BLONDEAU. Noise-enhanced nonlinear detector to improve signal detection in non-Gaussian noise. Signal Processing, vol. 86:3456–3465, 2006. 84/197
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