Scientists and engineers often seek to measure, communicate, store, process, reproduce, or analyze signals encountered in the real world. Most such signals are inherently continuous or analog in nature, yet increasingly the means for communicating, storing, and manipulating such information are discrete or digital. Generally something is lost when continuous information is converted into discrete approximations, so a natural goal is to preserve as much of the original information as possible. This is the general problem of quantization, a technique that historically has cropped up in a variety of branches of signal processing, taxonomy, physics, mathematics, and statistics as well as playing a key role as the interface between a continuous world and digital processing. Quantization traditionally has been used to model analog to digital conversion, Shannon source coding, and data compression. Viewed generally, quantization also models the extraction of information from signals, including statistical classification, clustering methods, and aspects of machine learning. This talk will describe the fundamentals of quantization along with examples and recent research topics in theory and application.

Robert M. Gray (F) received the B.S. and M.S. degrees from the Massachusetts Institute of Technology in 1966, and the Ph.D. degree from the University of Southern California in 1969, all in electrical engineering. Since 1969, he has been with Stanford University, where he is currently, the Lucent Technologies Professor of Engineering. His research interests are the theory and design of signal compression and classification systems.

Prof. Gray is the author of more than 200 papers and eight books, including "Vector Quantization and Signal Compression" with A. Gersho (Kluwer, 1992), "An Introduction to Statistical Signal Processing" with L. D. Davisson (Cambridge University Press, 2005), and "Stochastic Image Processing" with C.-S. Won (Springer/Kluwer/Plenum, 2004).

Prof. Gray served on the Board of Governors of the IEEE Information Theory Group (1974-80 and 1985-88) and IEEE Signal Processing Society (1998-2001). He was an Associate Editor (1977-80) and Editor-in-Chief (1980-83), IEEE Transactions on Information Theory; Co-chair, 1993 International Symposium on Information Theory; Technical Program Co-chair, 1997 and 2004 IEEE International Conference on Image Processing (ICIP); and Member and Chair, SPS Image and Multidimensional Signal Processing Technical Committee (1994-2003 and 2000-2001, respectively).

Prof. Gray was co-recipient with L.D. Davisson of the IEEE Information Theory Group Paper Award (1976) and co-recipient with A. Buzo, A.H. Gray, and J.D. Markel of the IEEE ASSP Senior Award (1983). He received the IEEE Signal Processing Society Award (1993), the Technical Achievement Award from the IEEE Signal Processing Society (1997), and a Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society (1998). He was awarded an IEEE Centennial Medal (1994) and an IEEE Third Millennium Medal (2000). Prof. Gray is a Fellow of the IEEE and the Institute of Mathematical Statistics and has held fellowships from the Japan Society for the Promotion of Science at the University of Osaka (1981), the Guggenheim Foundation at the University of Paris XI (1982), and NATO/Consiglio Nazionale delle Ricerche at the University of Naples (1990). During Spring 1995, he was a Vinton Hayes Visiting Scholar at the Division of Applied Sciences of Harvard University. He received a Presidential Award for Excellence in Science (2002) and Mathematics and Engineering Mentoring (PAESMEM) in the White House (March 2003).