Stochastic Resonance in Sequential Detectors

Stochastic resonance (SR) is a nonlinear phenomenon known in physics that has attracted recent interest in the signal-processing literature, and specifically in the context of detection. We investigate the SR effect arising in sequential detectors for shift-in-mean binary hypothesis testing and characterize the optimal resonance as the solution of specific optimization problems. One particular (and at first glance perhaps counterintuitive) finding is that certain sequential detection procedures can be made more efficient by randomly adding or subtracting a suitable constant value to the data at the input of the detector.

[1]  B. Kosko,et al.  Robust stochastic resonance: signal detection and adaptation in impulsive noise. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  P. Landa.  Mechanism of stochastic resonance , 2004 .

[3]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[4]  François Chapeau-Blondeau,et al.  Suprathreshold stochastic resonance and signal-to-noise ratio improvement in arrays of comparators [rapid communication] , 2004 .

[5]  Vincenzo Galdi,et al.  Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise , 1998 .

[6]  Bulsara,et al.  Nonlinear stochastic resonance: the saga of anomalous output-input gain , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  E. Paulson,et al.  A Note on the Efficiency of the Wald Sequential Test , 1947 .

[8]  L. Cam,et al.  Théorie asymptotique de la décision statistique , 1969 .

[9]  Mark D. McDonnell,et al.  Pooling networks for a discrimination task: noise-enhanced detection , 2007, SPIE International Symposium on Fluctuations and Noise.

[10]  Haralabos C. Papadopoulos,et al.  Sequential signal encoding from noisy measurements using quantizers with dynamic bias control , 2001, IEEE Trans. Inf. Theory.

[11]  Pierre-Olivier Amblard,et al.  Stochastic resonance in locally optimal detectors , 2003, IEEE Trans. Signal Process..

[12]  P Hänggi,et al.  Stochastic resonance in ion channels characterized by information theory. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  S. Kay,et al.  Can detectability be improved by adding noise? , 2000, IEEE Signal Processing Letters.

[14]  S. Kassam.  Signal Detection in Non-Gaussian Noise , 1987 .

[15]  Jan-Olof Gustavsson.  Detection in Non-Gaussian Noise , 1993 .

[16]  G. E. Noether,et al.  ON A THEOREM OF PITMAN , 1955 .

[17]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[18]  J. Andel.  Sequential Analysis , 2022, The SAGE Encyclopedia of Research Design.

[19]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[20]  Sawasd Tantaratana,et al.  On sequential sign detection of a constant signal , 1977, IEEE Trans. Inf. Theory.

[21]  François Chapeau-Blondeau,et al.  Stochastic resonance in the information capacity of a nonlinear dynamic system , 1998 .

[22]  Pierre-Olivier Amblard,et al.  On the use of stochastic resonance in sine detection , 2002, Signal Process..

[23]  Robert G. Gallager,et al.  Discrete Stochastic Processes , 1995 .

[24]  Lang Tong,et al.  Sensor networks with mobile agents , 2003, IEEE Military Communications Conference, 2003. MILCOM 2003..

[25]  Bart Kosko,et al.  Adaptive stochastic resonance in noisy neurons based on mutual information , 2004, IEEE Transactions on Neural Networks.

[26]  Pierre-Olivier Amblard,et al.  Quantizer-based suboptimal detectors: noise-enhanced performance and robustness (Invited Paper) , 2005, SPIE International Symposium on Fluctuations and Noise.

[27]  Pramod K. Varshney,et al.  Theory of the Stochastic Resonance Effect in Signal Detection—Part II: Variable Detectors , 2007, IEEE Transactions on Signal Processing.

[28]  N. U. Prabhu.  Review: D. R. Cox, H. D. Miller, The Theory of Stochastic Processes , 1966 .

[29]  Bulsara,et al.  Signal detection statistics of stochastic resonators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Peter Jung,et al.  STOCHASTIC RESONANCE AND OPTIMAL DESIGN OF THRESHOLD DETECTORS , 1995 .

[31]  F. Chapeau-Blondeau.  Nonlinear test statistic to improve signal detection in non-Gaussian noise , 2000, IEEE Signal Processing Letters.

[32]  Pierre-Olivier Amblard,et al.  On pooling networks and fluctuation in suboptimal detection framework , 2007 .

[33]  François Chapeau-Blondeau,et al.  Stochastic resonance and improvement by noise in optimal detection strategies , 2005, Digit. Signal Process..

[34]  Nigel G. Stocks,et al.  Suprathreshold stochastic resonance: an exact result for uniformly distributed signal and noise , 2001 .

[35]  J. Griffiths.  The Theory of Stochastic Processes , 1967 .

[36]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[37]  N G Stocks,et al.  Information transmission in parallel threshold arrays: suprathreshold stochastic resonance. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[39]  N. Stocks,et al.  Suprathreshold stochastic resonance in multilevel threshold systems , 2000, Physical review letters.

[40]  Derek Abbott,et al.  Stochastic resonance and data processing inequality , 2003 .

[41]  Bart Kosko,et al.  Stochastic resonance in noisy threshold neurons , 2003, Neural Networks.

[42]  François Chapeau-Blondeau,et al.  Noise-enhanced nonlinear detector to improve signal detection in non-Gaussian noise , 2006 .

[43]  Bart Kosko,et al.  Robust stochastic resonance for simple threshold neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  G. V. Anand,et al.  Design of detectors based on stochastic resonance , 2003, Signal Process..

[45]  Adi R. Bulsara,et al.  DC SIGNAL DETECTION VIA DYNAMICAL ASYMMETRY IN A NONLINEAR DEVICE , 1998 .

[46]  Sawasd Tantaratana,et al.  Relative efficiency of the sequential probability ratio test in signal detection , 1978, IEEE Trans. Inf. Theory.

[47]  Pramod K. Varshney,et al.  Theory of the Stochastic Resonance Effect in Signal Detection: Part I—Fixed Detectors , 2007, IEEE Transactions on Signal Processing.

[48]  Pramod K. Varshney,et al.  Reducing Probability of Decision Error Using Stochastic Resonance , 2006, IEEE Signal Processing Letters.

[49]  Aditya A. Saha.  Perturbative corrections to stochastic resonant quantizers , 2006 .

[50]  Pierre-Olivier Amblard,et al.  On stochastic resonance-like effect in detection , 2003, SPIE International Symposium on Fluctuations and Noise.

[51]  François Chapeau-Blondeau,et al.  Stochastic resonance for an optimal detector with phase noise , 2003, Signal Process..

[52]  François Chapeau-Blondeau,et al.  Noise-enhanced performance for an optimal Bayesian estimator , 2004, IEEE Transactions on Signal Processing.

[53]  Y. Bar-Shalom,et al.  Censoring sensors: a low-communication-rate scheme for distributed detection , 1996, IEEE Transactions on Aerospace and Electronic Systems.