Vector Space Projections

A guide to the theory and application of methods ofprojections.

With the rise of powerful personal computers, methods of vectorspace projections have moved rapidly from the realm of theory intowidespread use. This book reflects the growing interest in theapplication of these methods to problem solving in science andengineering. It brings together material previously scattered indisparate papers, book chapters, and articles, and offers asystematic treatment of vector space projections.

Written by two leading authorities in the field, thisself-contained volume provides a tutorial on projection methods andhow to apply them in science and engineering. It details effectiveproblem-solving strategies, and explores key applications incommunication and signal processing, neural networks and patternrecognition, and optics and image processing. This book:
* Reviews the fundamentals of vector space theory
* Covers principles and applications of vector space projections ingeneral, and projections onto convex sets in particular
* Provides real-world examples solvable on PCs and modestworkstations
* Features more than 100 illustrations
* Includes end-of-chapter exercises and references.

This extremely useful reference for practicing engineers,scientists, and educators can also be used for graduate-level studyin science, mathematics, and engineering. Portions of the book havebeen used as material in short courses on applications of vectorspace projections. Vector Space Concepts.

Projections Onto Convex Sets.

Elementary Projectors.

Solutions of Linear Equations.

Generalized Projections.

Applications to Communications.

Application to Optics.

Applications to Neural Nets.

Applications to Image Processing.

Index. "...a very useful addition among classical signal processingtexts...it can be warmly recommended..." (Analog Dialogue,Vol. 36, No. 5, September-October 2002) HENRY STARK is Bodine Professor and former chairman of theDepartment of Electrical and Computer Engineering at the IllinoisInstitute of Technology. He has written over 130 papers and bookchapters on topics ranging from image recovery and signalprocessing to neural nets and sampling theory. Professor Stark iscoauthor of Modern Electrical Communications and Probability,Random Processes, and Estimation Theory for Engineers and coeditorof Signal Processing Methods for Audio, Images, andTelecommunications.

YONGYI YANG is Assistant Professor at the Illinois Institute ofTechnology. He is a principal contributor to Signal ProcessingMethods for Audio, Images, and Telecommunications, coedited byHenry Stark. A guide to the theory and application of methods of projections.

With the rise of powerful personal computers, methods of vector space projections have moved rapidly from the realm of theory into widespread use. This book reflects the growing interest in the application of these methods to problem solving in science and engineering. It brings together material previously scattered in disparate papers, book chapters, and articles, and offers a systematic treatment of vector space projections.

Written by two leading authorities in the field, this self-contained volume provides a tutorial on projection methods and how to apply them in science and engineering. It details effective problem-solving strategies, and explores key applications in communication and signal processing, neural networks and pattern recognition, and optics and image processing. This book:

• Reviews the fundamentals of vector space theory
• Covers principles and applications of vector space projections in general, and projections onto convex sets in particular
• Provides real-world examples solvable on PCs and modest workstations
• Features more than 100 illustrations
• Includes end-of-chapter exercises and references.

This extremely useful reference for practicing engineers, scientists, and educators can also be used for graduate-level study in science, mathematics, and engineering. Portions of the book have been used as material in short courses on applications of vector space projections.