Robert M. Gray

Entropy and Information Theory

Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists. Highlights: Complete tour of book and guidelines for use given in Introduction, so readers can see at a glance the topics of interest. Structures mathematics for an engineering audience, with emphasis on engineering applications. New in the Second Edition: Much of the material has been rearranged and revised for pedagogical reasons. The original first chapter has been split in order to allow a more thorough treatment of basic probability before tackling random processes and dynamical systems. The final chapter has been broken into two pieces to provide separate emphasis on process metrics and the ergodic decomposition of affine functionals. Many classic inequalities are now incorporated into the text, along with proofs; and many citations have been added.

Probability, Random Processes, and Ergodic Properties

Jia Li

In the current age of information technology, the issues of distributing and utilizing images efficiently and effectively are of substantial concern. Solutions to many of the problems arising from these issues are provided by techniques of image processing, among which segmentation and compression are topics of this book. Image segmentation is a process for dividing an image into its constituent parts. For block-based segmentation using statistical classification, an image is divided into blocks and a feature vector is formed for each block by grouping statistics of its pixel intensities. Conventional block-based segmentation algorithms classify each block separately, assuming independence of feature vectors. Image Segmentation and Compression Using Hidden Markov Models presents a new algorithm that models the statistical dependence among image blocks by two dimensional hidden Markov models (HMMs). Formulas for estimating the model according to the maximum likelihood criterion are derived from the EM algorithm. To segment an image, optimal classes are searched jointly for all the blocks by the maximum a posteriori (MAP) rule. The 2-D HMM is extended to multiresolution so that more context information is exploited in classification and fast progressive segmentation schemes can be formed naturally. The second issue addressed in the book is the design of joint compression and classification systems using the 2-D HMM and vector quantization. A classifier designed with the side goal of good compression often outperforms one aimed solely at classification because overfitting to training data is suppressed by vector quantization. Image Segmentation and Compression Using Hidden Markov Models is an essential reference source for researchers and engineers working in statistical signal processing or image processing, especially those who are interested in hidden Markov models. It is also of value to those working on statistical modeling.

Image Segmentation and Compression Using Hidden Markov Models

Lee D. Davisson

This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

An Introduction to Statistical Signal Processing

Ergodic and Information Theory

This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.

In December 1974 the first realtime conversation on the ARPAnet took place between Culler- Harrison Incorporated in Goleta, California, and MIT Lincoln Laboratory in Lexington, Massachusetts. This was the first successful application of realtime digital speech communication over a packet network and an early milestone in the explosion of realtime signal processing of speech, audio, images, and video that we all take for granted today. It could be considered as the first voice over Internet Protocol (VoIP), except that the Internet Protocol (IP) had not yet been established. In fact, the interest in realtime signal processing had an indirect, but major, impact on the development of IP. This is the story of the development of linear predictive coded (LPC) speech and how it came to be used in the first successful packet speech experiments. Several related stories are recounted as well. The history is preceded by a tutorial on linear prediction methods which incorporates a variety of views to provide context for the stories. This part is a technical survey of the fundamental ideas of linear prediction that are important for speech processing, but the development departs from traditional treatments and takes advantage of several shortcuts, simplifications, and unifications that come with years of hindsight. In particular, some of the key results are proved using short and simple techniques that are not as well known as they should be, and it also addresses some of the common assumptions made when modeling random signals. The reader interested only in the history and already familiar with or uninterested in the technical details of linear prediction and speech may skip Part I entirely.

Robert M. Gray

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