Random Processes for Image Signal Processing

ISBN-13: 9780780334953 / Angielski / Twarda / 1998 / 616 str.

Edward R. Dougherty; Edward R. Daugherty

Opis

-This book gives readers an intuitive appreciation for random functions, plus theory and processes necessary for sophisticated applications. It covers probability theory, random processes, canonical representation, optimal filtering, and random models. Second in the SPIE/IEEE Series on Imaging Science & Engineering.

It also presents theory along with applications, to help readers intuitively appreciate random functions.

Included are special cases in which probabilistic insight is more readily achievable. When provided, proofs are in the main body of the text and clearly delineated; sometimes they are either not provided or outlines of conceptual arguments are given. The intent is to state theorems carefully and to draw clear distinctions between rigorous mathematical arguments and heuristic explanations. When a proof can be given at a mathematical level commensurate with the text and when it enhances conceptual understanding, it is usually provided; in other cases, the effort is to explain subtleties of the definitions and properties concerning random functions, and to state conditions under which a proposition applies. Attention is drawn to the differences between deterministic concepts and their random counterparts, for instance, in the mean-square calculus, orthonormal representation, and linear filtering. Such differences are sometimes glossed over in method books; however, lack of differentiation between random and deterministic analysis can lead to misinterpretation of experimental results and misuse of techniques.

The author's motivation for the book comes from his experience in teaching graduate-level image processing and having to end up teaching random processes. Even students who have taken a course on random processes have often done so in the context of linear operators on signals. This approach is inadequate for image processing. Nonlinear operators play a widening role in image processing, and the spatial nature of imaging makes it significantly different from one-dimensional signal processing. Moreover, students who have some background in stochastic processes often lack a unified view in terms of canonical representation and orthogonal projections in inner product spaces.-

Spis treści

Preface.

Probability Theory.

Random Processes.

Canonical Representation.

Optimal Filtering.

Random Models.

Bibliography.

Index.

O autorze

Edward R. Dougherty is director of the Imaging Division of the Texas Center for Applied Technology and professor of Electrical Engineering at Texas A&M University. He holds an MS in computer science from Stevens Institute of Technology and a PhD in mathematics from Rutgers University. He is author/coauthor of ten previous books and Editor of the SPIE/IS&T Journal of Electronic Imaging and of the SPIE/IEEE Series on Imaging Science and Engineering.

Blurb

Random Processes for Image and Signal Processing Edward R. Dougherty Second in the SPIE/IEEE Series on Imaging Science & Engineering Science and engineering deal with temporal, spatial, and higher–dimensional processes that vary randomly from observation to observation. Deterministic analysis does not provide a framework for understanding the ensemble of observations, nor does it provide a mechanism for predicting future events. Random processes provide the tools to bridge these gaps. Readers of this book will gain an intuitive appreciation of random functions, in addition to understanding theory and processes necessary for sophisticated applications. The initial chapter covers basic theory of probability, with special attention to multivariate distributions and functions of several random variables. Subsequent topics include the basic properties of random functions, canonical representation, transform coding, optimal filter design (linear and nonlinear), neural networks, discrete– and continuous–time Markov chains, and the theory of random closed sets. This book can be used as a one–semester course for students with a strong background in probability and statistics or as a full–year course for students who lack such preparation. The large number of imaging applications also makes it useful for graduate courses on image processing. Contents: Probability theory. Random processes. Canonical representation. Optimal filtering. Random models. Bibliography. Index.