Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization

by Mark D. McDonnell , Nigel G. Stocks , Charles E. M. Pearce , Derek Abbott

• ISBN13: 9780521882620
• ISBN10: 0521882621
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-10-27
• Publisher: Cambridge University Press

Summary

The stochastic resonance phenomenon has been observed in many forms of systems and has been debated by scientists for 30 years. Applications incorporating aspects of stochastic resonance have yet to prove revolutionary in fields such as distributed sensor networks, nano-electronics, and biomedical prosthetics. The initial chapters review stochastic resonance basics and outline some of the controversies and debates that have surrounded it. The book continues to discuss stochastic quantization in a model where all threshold devices are not necessarily identical, but are still independently noisy. Finally, it considers various constraints and tradeoffs in the performance of stochastic quantizers. Each chapter ends with a review summarizing the main points, and open questions to guide researchers into finding new research directions.

Author Biography

Derek Abbott is a Professor in the School of Electrical and Electronic Engineering at The University of Adelaide.

Table of Contents

List of figures	p. x
List of tables	p. xiv
Preface	p. xv
Foreword	p. xvii
Acknowledgments	p. xix
Introduction and motivation	p. 1
Background and motivation	p. 1
From stochastic resonance to stochastic signal quantization	p. 3
Outline of book	p. 4
Stochastic resonance: its definition, history, and debates	p. 6
Introducing stochastic resonance	p. 6
Questions concerning stochastic resonance	p. 9
Defining stochastic resonance	p. 10
A brief history of stochastic resonance	p. 14
Paradigms of stochastic resonance	p. 20
How should I measure thee? Let me count the ways...	p. 30
Stochastic resonance and information theory	p. 34
Is stochastic resonance restricted to subthreshold signals?	p. 39
Does stochastic resonance occur in vivo in neural systems?	p. 45
Chapter summary	p. 46
Stochastic quantization	p. 47
Information and quantization theory	p. 47
Entropy, relative entropy, and mutual information	p. 48
The basics of lossy source coding and quantization theory	p. 49
Differences between stochastic quantization and dithering	p. 52
Estimation theory	p. 58
Chapter summary	p. 58
Suprathreshold stochastic resonance: encoding	p. 59
Introduction	p. 59
Literature review	p. 61
Suprathreshold stochastic resonance	p. 67
Channel capacity for SSR	p. 101
SSR as stochastic quantization	p. 112
Chapter summary	p. 117
Suprathreshold stochastic resonance: large N encoding	p. 120
Introduction	p. 120
Mutual information when fx(x) = f¿(¿ - x)	p. 125
Mutual information for uniform signal and noise	p. 131
Mutual information for arbitrary signal and noise	p. 135
A General expression for large N channel capacity	p. 150
Channel capacity for 'matched' signal and noise	p. 158
Chapter summary	p. 163
Suprathreshold stochastic resonance: decoding	p. 167
Introduction	p. 167
Averaging without thresholding	p. 172
Linear decoding theory	p. 174
Linear decoding for SSR	p. 179
Nonlinear decoding schemes	p. 195
Decoding analysis	p. 206
An estimation perspective	p. 213
Output signal-to-noise ratio	p. 225
Chapter summary	p. 230
Suprathreshold stochastic resonance: large N decoding	p. 233
Introduction	p. 233
Mean square error distortion for large N	p. 234
Large N estimation perspective	p. 241
Discussion on stochastic resonance without tuning	p. 244
Chapter Summary	p. 246
Optimal stochastic quantization	p. 248
Introduction	p. 248
Optimal quantization model	p. 252
Optimization solution algorithms	p. 258
Optimal quantization for mutual information	p. 260
Optimal quantization for MSE distortion	p. 268
Discussion of results	p. 271
Locating the final bifurcation	p. 286
Chapter summary	p. 289
SSR, neural coding, and performance tradeoffs	p. 291
Introduction	p. 291
Information theory and neural coding	p. 296
Rate-distortion tradeoff	p. 309
Chapter summary	p. 321
Stochastic resonance in the auditory system	p. 323
Introduction	p. 323
The effect of signal distribution on stochastic resonance	p. 324
Stochastic resonance in an auditory model	p. 330
Stochastic resonance in cochlear implants	p. 344
Chapter summary	p. 356
The future of stochastic resonance and suprathreshold stochastic resonance	p. 358
Putting it all together	p. 358
Closing remarks	p. 360
Suprathreshold stochastic resonance	p. 362
Maximum values and modes of Py/x(n/x)	p. 362
A proof of Equation (4.38)	p. 363
Distributions	p. 363
Proofs that fQ (¿) is a PDF, for specific cases	p. 370
Calculating mutual information by numerical integration	p. 371
Large N suprathreshold stochastic resonance	p. 373
Proof of Eq. (5.14)	p. 373
Derivation of Eq. (5.18)	p. 374
Proof that fs(x) is a PDF	p. 375
Suprathreshold stochastic resonance decoding	p. 377
Conditional output moments	p. 377
Output moments	p. 378
Correlation and correlation coefficient expressions	p. 380
A proof of Prudnikov's integral	p. 382
Minimum mean square error distortion decoding	p. 385
Fisher information	p. 388
Proof of the information and Cramer-Rao bounds	p. 390
References	p. 392
List of abbreviations	p. 417
Index	p. 419
Biographies	p. 421
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