Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization
by Mark D. McDonnell , Nigel G. Stocks , Charles E. M. Pearce , Derek AbbottEdition: 1st
Format: Hardcover
Pub. Date: 2008-10-27
Publisher(s): Cambridge University Press
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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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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