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

  • 2020 Okawa Prize, The Okawa Foundation for Information and Telecommunications (2021)
  • Aaron D. Wyner Distinguished Service Award, IEEE Information Theory Society (2020)
  • Stanford University President's Award for Excellence through Diversity, Stanford University (2013)
  • Education Award, IEEE Signal Processing Society (2009)
  • Research Fellow, Michelle R. Clayman Institute for Gender Research, Stanford University (2008-2009)
  • Claude E. Shannon Award, IEEE Information Theoryt Society (2008)
  • Jack S. Kilby Signal Processing Medal, IEEE (2008)
  • Member, National Academy of Engineering (2007)
  • Distinguished Lecturer, IEEE Signal Processing Societyt (2006-2007)
  • Meritorious Service Award, IEEE Signal Processing Society (2005)
  • 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)
  • Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM), White House and NSF (2002)
  • Third Millennium Medal, IEEE (2000)
  • Golden Jubilee Award for Technological Innovation, IEEE Information Theory Society (1998)
  • Vinton Hayes Distinguished Visiting Scholar, Harvard University (1995)
  • Society Award, IEEE Signal Processing Society (1993)
  • Fellow, Institute for Mathematical Statistics (IMS) (1992)
  • Fellowship, NATO/Consiglio Nazionale delle Ricerche (1990)
  • Fellowship, University of Napoli, NATO/Consiglio Nazionale delle Ricerche (1990)
  • Centennial Medal, IEEE (1984)
  • Senior Award, IEEE Signal Processing Society (1983)
  • Fellowship, John Simon Guggenheim Foundation (1982)
  • Fellowship, Japan Society for the Promotion of Science (1981)
  • Fellow, IEEE (1980)
  • Prize Paper Award, IEEE Information Theory Group (1976)

Boards, Advisory Committees, Professional Organizations

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

Contact

  • Academic
    rmgray@stanford.edu
    University - Emeritus faculty Department: Electrical Engineering Position: Emeritus Faculty, Acad Council

Additional Info

Links

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

  • In Memory of AH "Steen" Gray Jr. IEEE SIGNAL PROCESSING MAGAZINE Gray, R. M. 2020; 37 (2): 96–100

    View details for DOI 10.1109/MSP.2019.2960460

    View details for Web of Science ID 000520154500009

  • Rate-Constrained Simulation and Source Coding i.i.d. Sources 2010 Data Compression Conference (DCC 2010) Mao, M. Z., Gray, R. M., Linder, T. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. 2011: 4516–29

    View details for DOI 10.1109/TIT.2011.2145930

    View details for Web of Science ID 000291922500034

  • On Asymptotically Optimal Stationary Source Codes for IID Sources Data Compression Conference (DCC) Mao, M. Z., Gray, R. M., Linder, T. IEEE COMPUTER SOC. 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 15th IEEE International Conference on Image Processing (ICIP 2008) Pyun, K. (., Lim, J., Gray, R. M. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. 2009: 1385–94

    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

    View details for DOI 10.1109/TIT.2008.920205

    View details for Web of Science ID 000255505700022

  • 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

    View details for DOI 10.1109/TIT.2007.915713

    View details for Web of Science ID 000253602200029

  • Rate-distortion functions for nonstationary Gaussian autoregressive processes 18th Data Compression Conference Gray, R. M., Hashimoto, T. IEEE COMPUTER SOC. 2008: 53–62

    View details for DOI 10.1109/DCC.2008.107

    View details for Web of Science ID 000255196800006

  • Bits in Asymptotically Optimal Lossy Source Codes are Asymptotically Bernoulli 19th Data Compression Conference Gray, R. M., Linder, T. IEEE COMPUTER SOC. 2008: 272–281

    View details for DOI 10.1109/DCC.2009.21

    View details for Web of Science ID 000268029900028

  • 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 32nd IEEE International Conference on Acoustics, Speech and Signal Processing Yoon, S., Gray, R. M. IEEE. 2007: 1081–1084

    View details for Web of Science ID 000248906600271

  • Quantization with joint entropy/memory constraints 16th Data Compression Conference Gray, R. M., Gill, J. T. IEEE COMPUTER SOC. 2006: 223–232

    View details for Web of Science ID 000236995300023

  • Entropy-based distortion measure for image coding 2006 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, ICIP 2006, PROCEEDINGS Andre, T., Antonini, M., Barlaud, M., Gray, R. M. 2006: 1157-?

    View details for Web of Science ID 000245768500290

  • Image compression with a vector speck algorithm 31st IEEE International Conference on Acoustics, Speech and Signal Processing Chao, C., Gray, R. M. IEEE. 2006: 1693–1696

    View details for Web of Science ID 000245559902070

  • Gauss mixture model-based classification for sensor networks 16th Data Compression Conference Ozonat, K., Gray, R. M. IEEE COMPUTER SOC. 2006: 322–331

    View details for Web of Science ID 000236995300033

  • Quantization in task-driven sensing and distributed processing 31st IEEE International Conference on Acoustics, Speech and Signal Processing Gray, R. M. IEEE. 2006: 5907–5910

    View details for Web of Science ID 000245559906180

  • Quantization in task-driven sensing and distributed processing 31st IEEE International Conference on Acoustics, Speech and Signal Processing Gray, R. M. IEEE. 2006: 1049–1052

    View details for Web of Science ID 000245100500263

  • Entropy and memory constrained vector quantization with separability based feature selection IEEE International Conference on Multimedia and Expo (ICME 2006) Yoon, S., Gray, R. M. IEEE. 2006: 269–272

    View details for Web of Science ID 000245384800068

  • ONE-PASS ADAPTIVE UNIVERSAL VECTOR QUANTIZATION 1994 IEEE International Conference on Acoustics, Speech and Signal Processing Effros, M., Chou, P. A., Gray, R. M. IEEE. 1994: 625–628

    View details for Web of Science ID A1994BC20L00156

  • IMAGE RECONSTRUCTION USING VECTOR QUANTIZED LINEAR INTERPOLATION 1994 IEEE International Conference on Acoustics, Speech and Signal Processing Hemami, S. S., Gray, R. M. IEEE. 1994: 629–632

    View details for Web of Science ID A1994BC20L00157

  • QUANTIZATION NOISE SPECTRA IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M. 1990; 36 (6): 1220-1244

    View details for Web of Science ID A1990EC43800003

  • SIGMA-DELTA MODULATION WITH IID GAUSSIAN INPUTS IEEE TRANSACTIONS ON INFORMATION THEORY Wong, P. W., Gray, R. M. 1990; 36 (4): 784-798

    View details for Web of Science ID A1990DL12900006

  • SPELLMODE RECOGNITION BASED ON VECTOR QUANTIZATION SPEECH COMMUNICATION Huang, S. S., Gray, R. M. 1988; 7 (1): 41-53

    View details for Web of Science ID A1988N090400003

  • 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

    View details for Web of Science ID A1987L785900010

  • ENCODING OF CORRELATED OBSERVATIONS IEEE TRANSACTIONS ON INFORMATION THEORY Flynn, T. J., Gray, R. M. 1987; 33 (6): 773-787

    View details for Web of Science ID A1987L785900003

  • OVERSAMPLED SIGMA-DELTA-MODULATION IEEE TRANSACTIONS ON COMMUNICATIONS Gray, R. M. 1987; 35 (5): 481-489

    View details for Web of Science ID A1987G916500001

  • 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

    View details for Web of Science ID A1986E908100008

  • BLOCK SOURCE-CODING THEORY FOR ASYMPTOTICALLY MEAN STATIONARY SOURCES IEEE TRANSACTIONS ON INFORMATION THEORY Gray, R. M., Saadat, F. 1984; 30 (1): 54-68

    View details for Web of Science ID A1984RX70300006

  • 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

    View details for Web of Science ID A1981MQ65800003

  • 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

    View details for Web of Science ID A1980KN45000010

  • 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

    View details for Web of Science ID A1980KF84400002

  • FAKE PROCESS APPROACH TO DATA COMPRESSION IEEE TRANSACTIONS ON COMMUNICATIONS Linde, Y., Gray, R. M. 1978; 26 (6): 840-847

    View details for Web of Science ID A1978FC79400011

  • 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

    View details for Web of Science ID A1977CW80600002

  • 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

    View details for Web of Science ID A1977CU67400007

  • UNBOUNDED TOEPLITZ MATRICES AND NONSTATIONARY TIME SERIES WITH AN APPLICATION TO INFORMATION-THEORY INFORMATION AND CONTROL Gray, R. M. 1974; 24 (2): 181-196

    View details for Web of Science ID A1974S138400006

  • SOURCE CODING FOR A SIMPLE NETWORK BELL SYSTEM TECHNICAL JOURNAL Gray, R. M., WYNER, A. D. 1974; 53 (9): 1681-1721

    View details for Web of Science ID A1974U656200001

https://orcid.org/0000-0002-6947-3637