Optimal Signal Processing Under Uncertainty

Description

In the classical approach to optimal filtering, it is assumed that the stochastic model of the physical process is fully known. For instance, in Wiener filtering it is assumed that the power spectra are known with certainty. The implicit assumption is that the parameters of the model can be accurately estimated. When models are complex or parameter estimation is difficult (or expensive), this assumption is unwarranted. With uncertain models, the natural solution is to optimize over both the original objective and the model uncertainty, thereby arriving at optimal robust operators, the topic of this book. The book also addresses the correlated problem of optimal experimental design: determining the experiment to perform in order to maximally reduce the uncertainty impacting the operational objective. Model uncertainty impacts a wide spectrum of disciplines: engineering, physics, biology, medicine, and economics. This book aims to provide the reader with a solid theoretical background to the state-of-the art in treating a problem that is only going to grow as our desire to control and make decisions regarding complex systems grows, and to do so by considering a broad set of topics: filtering, control, structural intervention, compression, classification, and clustering. Copyright......Page 5 Contents......Page 8 Preface......Page 12 Acknowledgments......Page 18 1 Random Functions......Page 20 2 Canonical Expansions......Page 42 3 Optimal Filtering......Page 70 4 Optimal Robust Filtering......Page 112 5 Optimal Experimental Design......Page 168 6 Optimal Classification......Page 216 7 Optimal Clustering......Page 268 References......Page 290 Index......Page 304 About the Author......Page 309