David Leigh Donoho

Quick Info

5 March 1957
Los Angeles, California, USA

David Donoho is a data scientist who had revolutionised the field, particularly with his concept of compressed sensing. He has received many awards including the Norbert Wiener Prize in Applied Mathematics 2010 and the Shaw Prize in Mathematics 2013.


David Donoho was the son of Paul Leighton Donoho (1931-2012) and Julia Arlene Haas (1931-2020). Paul Donoho, the son of David Hubert Leigh Donoho and Aletria Martelle Hicks, grew up in Houston, Texas, where he attended Lamar High School. He studied at Rice Institute in Houston (which became Rice University in 1960), graduating in 1952 with Honours in Physics. He then undertook research at the California Institute of Technology, marrying Julia Haas on 14 August 1954 in Los Angeles, California. He was still studying for his Ph.D. when his son David Leigh Donoho, was born in Los Angeles. Paul Donoho was awarded a Ph.D. in 1958 for his thesis Photoproduction of Positive K Mesons in Hydrogen having been examined by a committee that included Richard Feynman.

After a short spell at Bell Labs in New Jersey, the family moved to Houston, Texas when Paul Donoho was appointed to Rice University. Two further children were added to the family: Andrew Ward Donoho (born 11 August 1960 in Houston, Harris, Texas) and Julia Anne Donoho (born 13 August 1961 in Houston, Harris, Texas). Let us note at this point that Paul and Julia Donoho were divorced on 9 May 1979 and Paul married Merrily Pilot in 1982.

All of David Donoho's schooling was in Houston where his father was promoted steadily to become Professor of Physics at Rice University. David attended Robert E Lee High School in Houston, Texas, graduating 1974. This school, founded in 1960, has now been renamed as the Margaret Long Wisdom High School. Donoho writes [3]:-
I remember the chalk dust, slate blackboards and marble hallways of [my father's] academic office, and the lasers and low-temperature gadgets in his laboratory. Paul took our family on sabbatical to Grenoble, France, where I attended 6th grade - a transforming educational experience.
David was about eleven years old when the family went to France. Although he only spent one year at school in Grenoble, finding France had a very intense mathematical culture had a very large impact on his attitude towards mathematics. He said in the interview [36]:-
Also, seeing another culture and learning another language was very important.
For his university studies, Donoho's mother wanted him to go to Princeton, believing that it was the best university, and his father told him that he should definitely learn about computers because then he would always have a summer job in college because expertise in computers was good for finding employment. He followed his parents advice and when he got to Princeton he looked for a job in computer programming that would give him money to pay for his meals. He was given a job in the Statistics Department. His first task was to analyse data about people's use of energy in their homes. A massive data set was being collected and Donoho was hired as part of the data gathering. Later he became a manager of one of the first UNIX systems outside AT&T Bell Laboratories. John Tukey, the first Head of the Department of Statistics which was set up at Princeton in 1965, was also involved in the development of electronic computers at Bell Labs. Donoho was able to learn UNIX years before it became widely used. He wrote in [28]:-
I used three "statistics packages" while a Princeton undergraduate. P-STAT was an SPSS-like mainframe package which I used on Princeton's IBM 360/91 Mainframe; ISP was a UNIX minicomputer package on which I worked as a co-developer for the Princeton Statistics Department; and my teacher Don McNeil had developed software for a book of his own on exploratory data analysis; this ultimately became SPIDA after he moved to Macquarie University.
In fact while an undergraduate he wrote Documentation for ISP (Interactive Statistical Processor) (1977) for the Department of Statistics at Princeton University. In the summer of 1977 he worked as a programmer for University of Texas Marine Science Institute. The work he undertook involved programming a minicomputer for real-time detection and location of seismic events using data from seismic arrays in Costa Rica. He graduated from Princeton University with an A.B. in Statistics in 1978 having written an undergraduate thesis with John Tukey as his advisor.

After graduating from Princeton, Donoho was employed in the oil exploration business in Houston, Texas, as a Research Geophysicist at the Western Geophysical Company. The Company had just gone digital and with massive amounts of seismic data they needed algorithms to handle the large data sets. He implemented robust regression to work with data in thousands of rows and columns. During this time he lived at home and signed his pay cheque over to his father every month to pay him back for the college tuition fees he had paid. During the time he worked for the Western Geophysical Company he was sent to London, England, for several months so he could work with the Saudi Arabian oil company Aramco. It was an interesting time showing Aramco the robust methods he had developed, but he also found time to enjoy visits to many art museums and plays in London.

In 1979 Donoho enrolled at Harvard University to study for a Ph.D. His thesis advisor at Harvard was Peter Jost Huber, a Swiss mathematician who had started his career as a topologist with Beno Eckmann and Heinz Hopf as his thesis advisors, but had changed to statistics. Huber, one of the three main founders of robust statistics, had been appointed as Professor of Statistics at Harvard in 1978. He wrote the first systematic, book-length, description of robust statistics with his book Robust Statistics which he had in draft form in 1972 and was completed in 1980. Donoho talked about Huber in [36]:-
He was a very stimulating and interesting man and you could have many interesting conversations with him over tea. He was very interested in computers at the time and decided that the ideas of John Tukey, who had been my undergraduate advisor, were really the right ones, that you should be visualising data, using computer graphics. Peter was very interested in getting modern computer graphics to visualise data. I worked with my other co-students on various computer graphics. At the same time I couldn't stay away from ideas I had learnt about in my industrial research.
Donoho wrote the 70-page Ph.D. Qualifying Paper Breakdown properties of multivariate location estimators which was accepted in April 1982. The paper [19]:-
... exhibits coordinate-free estimators of multivariate location which can withstand up to 50% contamination of the data before breaking down. These include affine- equivariant generalisations of trimmed means and W-estimates, and a new minimum-distance estimator.
He was awarded a Ph.D. in 1983 for his 418-page thesis DART: A Tool for Research in Data Analysis. In it he [19]:-
... describes the design and implementation of a compact data analysis language. The uses of the language for constructing advanced systems for multivariate graphics are described.
While at Harvard, Donoho had met Miriam Gasko (born 22 May 1945) who was also undertaking research at Harvard for a Ph.D. in statistics. She was awarded a Ph.D. in 1981 for her thesis Testing Sequentially Selected Outliers from Linear Models. She published papers with Arthur Pentland Dempster, who worked at the Department of Statistics at Harvard from its founding in 1957, such as New Tools for Residual Analysis (1981). Donoho and Gasko published the joint paper Influential observations in data analysis (1982) by which time Gasko was at the University of Chicago.

After the award of his doctorate in 1983, Donoho was appointed as NSF Postdoctoral Fellow in the Department of Statistics at the University of California, Berkeley. He held this postdoctoral fellowship for the two years 1983-85, but in 1984 he was appointed as an Assistant Professor in the Department of Statistics at Berkeley. Also in 1984 Donoho and Gasko were married. They had a son Daniel Aharon Donoho, born in 1985, who was awarded a B.A. from Dartmouth College (2006) and a medical degree from the State University of New York at Stony Brook (2013). He became a neurosurgeon who develops machine learning systems to make surgery safer.

In 1985 David Donoho was awarded the Presidential Young Investigator Award by the National Science Foundation. This prestigious award gave him funds to support his research for five years. He used funding from the award to run a conference for research statisticians from Eastern Europe, Germany and France. For information about this award and other awards made to Donoho see THIS LINK.

Also in 1985, Donoho, together with his brother Andrew Donoho and his wife Miriam Gasko. published MacSpin: Graphical Data Analysis comprising of a book and a computer graphics system. The MacSpin system was produced by D2, a company founded by Donoho to produce the software. MacSpin received the award "MacSpin - Best Scientific/Engineering Software of 1987," from the MacUser Magazine. You can read a version of the MacUser review [49] of the first version of MacSpin at THIS LINK.

Donoho was promoted rapidly at the University of California, Berkeley: Assistant Professor of Statistics (1984-86); Associate Professor of Statistics (1987-1990); and Professor of Statistics (1990-1997). He wrote about his research during these years in [3]:-
At Berkeley during my postdoctoral and junior faculty years (1985-1990), I was in the Mecca of classical mathematical statistics, but I pursued my 'non-classical' interests. Iain Johnstone and I showed how to optimally 'denoise' sparse signals observed in noise, injecting 'sparsity' into top statistics journals. A sparse signal sticks up here and there above the noise, like daisies above weeds; our denoiser, based on l1l_{1}-minimization, chops away the weeds while leaving the daisies. Jeff Hoch and Alan Stern successfully applied such ideas in Magnetic Resonance spectroscopy. To publish 'non-classical' work on undersampled measurements of sparse signals, I turned to applied mathematics journals.
In 1991 he was appointed as Professor in the Department of Statistics of Stanford University. He was officially named to the Anne T and Robert M Bass Professorship in the School of Humanities and Sciences of Stanford University in a ceremony in the Iris & B Gerald Cantor Center for Visual Arts on Wednesday 29 May 2002 attended by friends, family, and colleagues. In addition to these appointments, Donoho has been a Visiting Professor at CNRS, Université de Paris XI, in the summer of 1986, at the Université de Paris VII in 1992, and at the Université de Paris XI in 1998. He was a Sackler Fellow at Tel Aviv University in 2000, Kloosterman Professor at the University of Leiden in 2002, and Rothschild Visiting Professor and Rothschild Lecturer at the University of Cambridge in 2008.

Donoho's work has covered a very broad spectrum and has had applications in many important areas. We give the following short summary from [27]:-
David Donoho has studied the exploitation of sparse signals in signal recovery, including for denoising, superresolution, and solution of underdetermined equations. He coined the notion of compressed sensing which has impacted many scientific and technical fields, including magnetic resonance imaging in medicine, where it has been implemented in FDA-approved medical imaging protocols and is already used in millions of actual patient MRIs. In recent years he has been studying large-scale covariance matrix estimation, large-scale matrix denoising, detection of rare and weak signals among many pure noise non-signals, compressed sensing and related scientific imaging problems, and most recently, empirical deep learning.
For details of his work over the last 20 years, see the abstracts of ten lectures he has given at THIS LINK.

There are other aspects of Donoho's career that we should mention. We have seen a list of over 25 patents issued by the United States Patent and Trademark Office, U.S. which involve Donoho. They all list other colleagues, for example David Salim Hindawi (born December 1944) who was president of BigFix Inc. and Lisa Ellen Lippincott who was awarded a Ph.D. by the University of California Berkeley in 1994 for her thesis A Complete System of Proof for Diagrammatic Languages. The company BigFix Inc. was founded in April 1997 in Emeryville, California by David Hindawi and David Donoho [54]:-
The company's initial product was a user self-service system management application that was marketed to Original Equipment Manufacturer PC manufacturers. In 2002, the company developed BigFix software for company-wide networked desktop, mobile and server computer management. This shifted the focus of the company from consumer to enterprise markets. Initial uses centred on security patch management, which was identified as a significant pain point at that time for enterprise IT departments. In 2007, BigFix expanded to specific management areas: security threat suppression (BigFix Endpoint Protection), enterprise security configuration management (BigFix Security Configuration and Vulnerability Management) and enterprise systems management (BigFix Systems Lifecycle Management).
Donoho writes in [19] that he was:-
... co-founder of BigFix.com, a Berkeley, CA start-up aiming to fundamentally change the practice of technical support for computers and associated network-connected devices. As disclosed in several US Patents, BigFix has developed a new internet communications model with profound implications for the high tech sector, implications reaching far beyond the initial applications in technical support.
The company BigFix Inc. was acquired by IBM in 2010 for about $400,000,000.

For his remarkable work Donoho has been awarded many prizes and honours. He has been awarded the Presidential Young Investigator Award 1985, made a MacArthur Fellow 1991, given the Committee of Presidents of Statistical Societies Presidents' Award 1994, the SIAM John von Neumann Lecture Prize 2001, and the Information Theory Society Paper Award 2008. This was awarded for his paper Compressed Sensing (2006) which [3]:-
... explained that, because the wavelet transform sparsifies images, images can be recovered from relatively few random measurements via l1l_{1} minimization.
He received the Norbert Wiener Prize in Applied Mathematics 2010 [51]:-
... for introducing novel fundamental and powerful mathematical tools in signal processing and image analysis. His many outstanding contributions include those to compressed sensing and the construction of multiscale analysis techniques that take advantage of the specific mathematical and physical properties of the problems under consideration. His methods are very deep mathematically and very efficient computationally. This explains their success with both theoreticians and practitioners, which causes him to be one of the most cited applied and computational mathematicians of our time.
Donoho was awarded the Shaw Prize in 2013 [23]:-
... for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.
The Gauss Prize for 2018 was awarded to David Donoho [45]:-
... for his fundamental contributions to the mathematical, statistical and computational analysis of signal processing.
David Donoho was awarded the Jack S Kilby Signal Processing Medal by the Institute of Electrical and Electronics Engineers in 2022 [1]:-
... for groundbreaking contributions to sparse signal recovery and compressed sensing.
For more information about all these awards and prizes given to Donoho, see THIS LINK.

Some other awards include the following. In 2008 he was awarded the Information Theory Paper Award from the Institute of Electrical and Electronics Engineers. The purpose of the Information Theory Paper Award is to recognise exceptional publications in the field and to stimulate interest in and encourage contributions to fields of interest of the Society. On 7 June 2011 the publisher Elsevier announced the winners of the Executable Paper Grand Challenge [34]:-
Matan Gavish and David Donoho, Stanford University, received third prize for "A Universal Identifier for Computational Results". The Universal Identifier is a specific implementation of one aspect the executable paper - an ID resolution system for results. The proposed solution is simple and elegant, and confers ease of use by adding one or two lines of code.
Other honours given to Donoho include: election to the American Academy of Arts and Sciences (1992); election to the National Academy of Sciences, USA (1998); election as Foreign Associate of the Académie des Sciences (2010); and election to the American Philosophical Society (2019). He was awarded an honorary Doctor of Science from the University of Chicago (2009), a Doctor Honoris Causa from the École Polytechnique Fédérale de Lausanne (2012), an honorary Doctor of Science from the University of Waterloo (2016), and an honorary Doctor of Science from Technion (2017). The first of these honorary degrees was from the University of Chicago [17]:-
On 9 October David L Donoho received the honorary degree of Doctor of Science from The University of Chicago. The occasion was a special convocation, the 500th in the university's history, and Donoho's was one of four degrees awarded. In presenting the degree, the university's president - mathematician Robert Zimmer - said, "David L Donoho is a mathematical statistician and also one of the more influential applied mathematicians of his generation. Building upon the discipline of statistics, Donoho has developed effective new approaches to constructing low-dimensional representations for modern high-dimensional data problems. His work provides new insight into some of the most pressing scientific questions of the present day."
Perhaps the most impressive of all is that Donoho was named as the most cited mathematician in the decade of the 1990s. He was named most highly-cited author in the field of Mathematics in the decade of the 1990 by Institute for Scientific Information, makers of the Science Citation Index and associated citation services. The Institute for Scientific Information methodology counted citations in all fields of science and engineering to the 200 most-cited papers in mathematics in each year 1990-1999. Donoho was the author of ten such highly-cited papers, also the most among mathematicians.

Donoho commented in 2018 [14]:-
There are things I've done decades ago, and when I see things happen in the real world, it makes me so proud. The power we have in moving the world gives me a great deal of satisfaction in my career choice. ... There are so many relations between mathematics and the rest of the world. We see more and more relations over time; so much in the modern world is underpinned by mathematics, for example smartphones, and the vast level of mathematical fundamentals intertwined, such as prime factorisation.
Let us end with some comments taken from the talk by his colleague Emmanuel Candès's (with some reformatting) [4]:-
David Donoho is a modern polymath who informs himself about everything: science, engineering, policy making ..., tries to understand what people are doing successfully, and develops insightful mathematics - to understand why things work/don't work - to create new models for data - to create new processing algorithms - and to ultimately inspire real concrete improvements; e.g. in human health.

David Donoho is a 'physicist of information' who is a deep mathematical thinker who tirelessly informs himself about what others are doing successfully. This requires extra effort, it is not easy. He sets the course/agenda and is in the lineage of intellectual giants like Euler, Gauss, Poincaré, Wiener, Kolmogorov, and von Neumann.

References (show)

  1. 2022 IEEE Jack S Kilby Signal Processing Medal for David Donoho, Department of Statistics, Stanford University (1 March 2022).
  2. An Essay on the Prize: David L Donoho, The Shaw Prize (2013).
  3. Autobiography of David Donoho, The Shaw Prize (2013).
  4. E Candès, The Work of David Donoho, International Congress of Mathematicians 2018 Rio de Janeiro.
  5. Contribution of David L Donoho, The Shaw Prize (2013).
  6. Dave Donoho: CV, Stanford University (2024).
  7. Dave Donoho: Home, Stanford University (2024).
  8. Dave Donoho: Lectures, Stanford University (2024).
  9. Dave Donoho: Publications, Stanford University (2024).
  10. David Donoho, Mathematics Research Center, Stanford University (2024).
  11. David Donoho, Clay Mathematics Institute (2024).
  12. David Donoho, American Academy of Arts & Sciences (2024).
  13. David Donoho, Prabook.com (2024).
  14. David Donoho's Gauss Award, Institute of Mathematical Statistics (1 October 2018).
  15. David Donoho '78 Receives 2018 Gauss Prize at ICM, Department of Mathematics, Princeton University (2018).
  16. David Donoho: Class of 1991, MacArthur Foundation (1991).
  17. David L Donoho Receives Honorary Degree, Amstat News (1 December 2009).
  18. David L Donoho, National Academy of Sciences (2014).
  19. David L Donoho, Resumé, School of Computer Science, Tel Aviv University (2024).
  20. David L Donoho, Engineering and Technology History Wiki (11 April 2022).
  21. David Sprott Distinguished Lecture by Professor David Donoho, Statistics and Actuarial Science, University of Waterloo (20 October 2016).
  22. Distinguished Lecture by David L Donoho, Georgia Tech (5 September 2018).
  23. Donoho Awarded 2013 Shaw Prize, Notices of the American Mathematical Society 61 (3) (2014), 284-285.
  24. Donoho Awarded Gauss Prize, Notices of the American Mathematical Society 65 (1) (2018), 1440.
  25. Donoho and Figalli Recognized at ICM 2018, Institute for Pure and Applied Mathematics (7 August 2018).
  26. D Donoho, From blackboard to bedside - Gauss Prize Lecture, Proceedings of the International Congress of Mathematicians 2018 Rio de Janeiro 1 (2018), 211-224.
  27. D Donoho, Data Science at the Singularity, International Conference on Statistics and Data Science 2023 (19 December 2023).
  28. D Donoho, 50 Years of Data Science, Tukey Centennial workshop, Princeton NJ (18 September 2015).
  29. D L Donoho, David Sprott Distinguished Lecture: Factor Models and PCA in light of the spiked covariance model, University of Waterloo (20 October 2016).
  30. D L Donoho, Deepnet Spectra and the Two Cultures of Data Science, King Abdullah University of Science and Technology (12 November 2019).
  31. D L Donoho, Compressed Sensing: From Theory to Practice, The 2016-2017 Dean W Lytle Lecture Series, University of Washington (7 November 2016).
  32. D L Donoho, High-dimensional statistics in light of the spiked covariance model, The 2016-2017 Dean W Lytle Lecture Series, University of Washington (8 November 2016).
  33. D L Donoho, The Romance of Hidden Components, Institute for Mathematical Sciences Public Lecture, Institute for Mathematical Sciences (25 August 2004).
  34. Elsevier announces winners of the Executable Paper Grand Challenge, EurekAlert!, American Association for the Advancement of Science (7 June 2011).
  35. Health Data Science Distinguished Speaker Series: Dr David Donoho, Stanford University, School of Public Health, Boston University (15 May 2024).
  36. IAS Interview with Prof David Donoho, youtube.com.
  37. Information Theory Society Paper Award: David Donoho, IEEE Information Theory Society (2024).
  38. M Kelly, Alumnus Donoho receives Shaw Prize in mathematics, Princeton University (28 May 2013).
  39. J Langston, Electrical engineering lecture series to explore compressed sensing, University of Washington (3 November 2016).
  40. X Lin, C Genest, D L Banks, G Molenberghs, D W Scott and J-L Wang (eds.), Past, Present and Future of Statistical Science (CRC Press, 2014).
  41. Miriam and David Donoho Academy of Clinical & Educational Scholars, Renaissance School of Medicine, Stony Brook University (2023).
  42. S Muthukrishnan, Q&A: Professor David Donoho discusses mathematics of mass testing, The Stanford Daily (29 July 2020).
  43. Paul Leighton Donoho: Obituary, Houston Chronicle (8 July 2012).
  44. The Gauss Prize 2018: David Donoho, Plus Magazine (5 August 2018).
  45. The Gauss Prize 2018: David Donoho, The International Mathematical Union (2018).
  46. The Shaw Prize in Mathematics 2013: David L Donoho, The Shaw Prize (2013).
  47. TRIPODS Distinguished Lecture by David Donoho: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise, Institute of Data Science, Texas A&M University (14 October 2021).
  48. David Donoho named MacArthur Fellow, Stanford University News Service, Stanford University (18 June 1991).
  49. E Hirame, Look At It This Way, MacUser 1 (9) (June 1986), 40-44.
  50. David Donoho appointed to Bass Chair, Department of Statistics, Stanford University (29 May 2002).
  51. David Donoho awarded 2010 Wiener Prize, IMS Bulletin 39 (7) (2010), 3.
  52. 2010 Wiener Prize, Notices of the American Mathematical Society 57 (4) (2010), 519-520.
  53. David Leigh Donoho, in American Men & Women of Science. A biographical dictionary of today's leaders in physical, biological and related sciences (33rd Edition) (Cengage Learning, Detroit, 2015).
  54. Company: BigFix Inc, HandWiki.

Additional Resources (show)

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Written by J J O'Connor and E F Robertson
Last Update June 2024