Bio


Robert M. Gray is the Alcatel-Lucent Technologies Professor of Communications and Networking in the School of Engineering, Emeritus, and Professor of Electrical Engineering, Emeritus, at Stanford University. He is a Fellow of the IEEE and the Institute for Mathematical Statistics and he was a 1981--82 Fellow of the John Simon Guggenheim Foundation. His professional awards include an Education Award, Meritorious Service Award, Technical Achievement Award, and Society award from the IEEE Signal Processing Society, a Golden Jubilee Award for Technological Innovation and the Claude E. Shannon Award from the IEEE Information Theory Society, and the Jack S. Kilby Signal Processing Medal and Centennial and Third Millennium Medals from the IEEE. He received a Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM). He is a member of the National Academy of Engineering. He retired from Stanford in April 2013 and is currently a Research Professor at Boston University.

Academic Appointments


Honors & Awards


  • Research Fellow, Michelle R. Clayman Institute for Gender Research, Stanford University (2008-2009)
  • First Lucent Technologies Chair in Communications and Networking in the School of Engineering, Stanford University (2004)
  • Distinguished Alumni in Academia Award, University of Southern California (2003)
  • Vinton Hayes Distinguished Visiting Scholar, Harvard University (1995)
  • Fellowship, NATO/Consiglio Nazionale delle Ricerche (1990)
  • Fellowship, John Simon Guggenheim Foundation (1982)
  • Fellowship, Japan Society for the Promotion of Science (1981)
  • Fellow, Institute for Mathematical Statistics (IMS) (1992)
  • Third Millennium Medal, IEEE (2000)
  • Centennial Medal, IEEE (1984)
  • Distinguished Lecturer, IEEE Signal Processing Societyt (2006-2007)
  • Education Award, IEEE Signal Processing Society (2009)
  • Meritorious Service Award, IEEE Signal Processing Society (2005)
  • Society Award, IEEE Signal Processing Society (1993)
  • Senior Award, IEEE Signal Processing Society (1983)
  • Prize Paper Award, IEEE Information Theory Group (1976)
  • Golden Jubilee Award for Technological Innovation, IEEE Information Theory Society (1998)
  • Fellow, IEEE (1980)
  • Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM), White House and NSF (2002)
  • Jack S. Kilby Signal Processing Medal, IEEE (2008)
  • Claude E. Shannon Award, IEEE Information Theoryt Society (2008)
  • Member, National Academy of Engineering (2007)

Boards, Advisory Committees, Professional Organizations


  • Editor-in-Chief, Transactions on Information Theory, IEEE (1981 - 1983)

Current Research and Scholarly Interests


My current research falls in the intersection of Shannon information theory and signal processing. In particular, I am interested in the theory and design of block codes and sliding-block (or stationary or time-invariant) codes for data compression and their relation to each other. Block codes are far better understood and more widely used, but their lack of stationarity causes difficulties in theory and artifacts in practice. Very little is known about the design of good sliding-block codes, but the problem is known to be equivalent to the design of entropy-constrained simulators of complex random processes. I also do research in the history of information theory and signal processing, especially in the development of speech processing systems and real time signal processing.

All Publications


  • Rate-Constrained Simulation and Source Coding i.i.d. Sources IEEE TRANSACTIONS ON INFORMATION THEORY Mao, M. Z., Gray, R. M., Linder, T. 2011; 57 (7): 4516-4529
  • On Asymptotically Optimal Stationary Source Codes for IID Sources 2011 DATA COMPRESSION CONFERENCE (DCC) Mao, M. Z., Gray, R. M., Linder, T. 2011: 3-12

    View details for DOI 10.1109/DCC.2011.8

    View details for Web of Science ID 000298610800001

  • A Robust Hidden Markov Gauss Mixture Vector Quantizer for a Noisy Source IEEE TRANSACTIONS ON IMAGE PROCESSING Pyun, K. (., Lim, J., Gray, R. M. 2009; 18 (7): 1385-1394

    Abstract

    Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.

    View details for DOI 10.1109/TIP.2009.2019433

    View details for Web of Science ID 000267221900001

    View details for PubMedID 19457751

  • Real-world image annotation and retrieval: An introduction to the special section IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Wang, J. Z., Geman, D., Luo, J., Gray, R. M. 2008; 30 (11): 1873-1876

    View details for Web of Science ID 000259110000001

    View details for PubMedID 19791313

  • Lagrangian vector quantization with combined entropy and codebook size constraints IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M., Linder, T., Gill, J. T. 2008; 54 (5): 2220-2242
  • A note on rate-distortion functions for nonstationary Gaussian autoregressive processes IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M., Hashimoto, T. 2008; 54 (3): 1319-1322
  • Rate-distortion functions for nonstationary Gaussian autoregressive processes DCC: 2008 DATA COMPRESSION CONFERENCE, PROCEEDINGS Gray, R. M., Hashimoto, T. 2008: 53-62
  • Bits in Asymptotically Optimal Lossy Source Codes are Asymptotically Bernoulli DCC 2009: 2009 DATA COMPRESSION CONFERENCE, PROCEEDINGS Gray, R. M., Linder, T. 2008: 272-281
  • Entropy-based distortion measure and bit allocation for wavelet image compression IEEE TRANSACTIONS ON IMAGE PROCESSING Andre, T., Antonini, M., Barlaud, M., Gray, R. M. 2007; 16 (12): 3058-3064

    View details for DOI 10.1109/TIP.2007.909408

    View details for Web of Science ID 000251295700017

    View details for PubMedID 18092603

  • Image segmentation using hidden Markov Gauss mixture models IEEE TRANSACTIONS ON IMAGE PROCESSING Pyun, K. (., Lim, J., Won, C. S., Gray, R. M. 2007; 16 (7): 1902-1911

    Abstract

    Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

    View details for DOI 10.1109/TIP.2007.899612

    View details for Web of Science ID 000247489200018

    View details for PubMedID 17605387

  • Clustering and finding the number of clusters by unsupervised learning of mixture models using vector quantization 2007 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL III, PTS 1-3, PROCEEDINGS Yoon, S., Gray, R. M. 2007: 1081-1084
  • Quantization with joint entropy/memory constraints DCC 2006: DATA COMPRESSION CONFERENCE, PROCEEDINGS Gray, R. M., Gill, J. T. 2006: 223-232
  • Quantization in task-driven sensing and distributed processing 2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13 Gray, R. M. 2006: 5907-5910
  • Image compression with a vector speck algorithm 2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13 Chao, C., Gray, R. M. 2006: 1693-1696
  • Gauss mixture model-based classification for sensor networks DCC 2006: DATA COMPRESSION CONFERENCE, PROCEEDINGS Ozonat, K., Gray, R. M. 2006: 322-331
  • Quantization in task-driven sensing and distributed processing 2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL V, PROCEEDINGS Gray, R. M. 2006: 1049-1052
  • Entropy and memory constrained vector quantization with separability based feature selection 2006 IEEE INTERNATIONAL CONFERENCE ON MULTIMEDIA AND EXPO - ICME 2006, VOLS 1-5, PROCEEDINGS Yoon, S., Gray, R. M. 2006: 269-272
  • IMAGE RECONSTRUCTION USING VECTOR QUANTIZED LINEAR INTERPOLATION ICASSP-94 - PROCEEDINGS, VOL 5 Hemami, S. S., Gray, R. M. 1994: 629-632
  • ONE-PASS ADAPTIVE UNIVERSAL VECTOR QUANTIZATION ICASSP-94 - PROCEEDINGS, VOL 5 Effros, M., Chou, P. A., Gray, R. M. 1994: 625-628
  • QUANTIZATION NOISE SPECTRA IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M. 1990; 36 (6): 1220-1244
  • SIGMA-DELTA MODULATION WITH IID GAUSSIAN INPUTS IEEE TRANSACTIONS ON INFORMATION THEORY Wong, P. W., Gray, R. M. 1990; 36 (4): 784-798
  • SPELLMODE RECOGNITION BASED ON VECTOR QUANTIZATION SPEECH COMMUNICATION Huang, S. S., Gray, R. M. 1988; 7 (1): 41-53
  • THE DESIGN OF JOINT SOURCE AND CHANNEL TRELLIS WAVEFORM CODERS IEEE TRANSACTIONS ON INFORMATION THEORY Ayanoglu, E., Gray, R. M., Gray, R. M. 1987; 33 (6): 855-865
  • ENCODING OF CORRELATED OBSERVATIONS IEEE TRANSACTIONS ON INFORMATION THEORY Flynn, T. J., Gray, R. M. 1987; 33 (6): 773-787
  • OVERSAMPLED SIGMA-DELTA-MODULATION IEEE TRANSACTIONS ON COMMUNICATIONS Gray, R. M. 1987; 35 (5): 481-489
  • SHAPE-GAIN MATRIX QUANTIZERS FOR LPC SPEECH IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING Tsao, C., Gray, R. M. 1986; 34 (6): 1427-1439
  • BLOCK SOURCE-CODING THEORY FOR ASYMPTOTICALLY MEAN STATIONARY SOURCES IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M., Saadat, F. 1984; 30 (1): 54-68
  • RATE-DISTORTION SPEECH CODING WITH A MINIMUM DISCRIMINATION INFORMATION DISTORTION MEASURE IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M., GRAY, A. H., REBOLLEDO, G., SHORE, J. E. 1981; 27 (6): 708-721
  • SPEECH CODING BASED UPON VECTOR QUANTIZATION IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING BUZO, A., GRAY, A. H., Gray, R. M., MARKEL, J. D. 1980; 28 (5): 562-574
  • DISTORTION MEASURES FOR SPEECH PROCESSING IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING Gray, R. M., BUZO, A., GRAY, A. H., Matsuyama, Y. 1980; 28 (4): 367-376
  • FAKE PROCESS APPROACH TO DATA COMPRESSION IEEE TRANSACTIONS ON COMMUNICATIONS Linde, Y., Gray, R. M. 1978; 26 (6): 840-847
  • COMPARISON OF OPTIMAL QUANTIZATIONS OF SPEECH REFLECTION COEFFICIENTS IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING GRAY, A. H., Gray, R. M., MARKET, J. D. 1977; 25 (1): 9-23
  • TIME-INVARIANT TRELLIS ENCODING OF ERGODIC DISCRETE-TIME SOURCES WITH A FIDELITY CRITERION IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M. 1977; 23 (1): 71-83
  • SOURCE CODING FOR A SIMPLE NETWORK BELL SYSTEM TECHNICAL JOURNAL Gray, R. M., WYNER, A. D. 1974; 53 (9): 1681-1721
  • UNBOUNDED TOEPLITZ MATRICES AND NONSTATIONARY TIME SERIES WITH AN APPLICATION TO INFORMATION-THEORY INFORMATION AND CONTROL Gray, R. M. 1974; 24 (2): 181-196