Optimal Signal Processing Under Uncertainty

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.