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Ingrid Daubechies

Professor Daubechies' primary area of research is harmonic analysis guided by problems that arise in science, engineering, and psychology. By learning about the concerns of scientists and engineers, Prof. Daubechies works to abstract the underlying mathematical problems and then solve them with analysis.

She has worked extensively on problems related to signal analysis. One of her major areas of interest in this field is the wavelet transform. Wavelets provide a mathematical representation of a complex signaling pattern from a series of simpler building blocks. To these one can add increasingly fine and increasingly localized detail, much in the same way a painter uses smaller brushes to achieve a greater degree of detail. Her work led her to construct a family of "compactly supported" wavelets known as the "Daubechies Wavelets." This has opened the door for a new system of image compression that allows for the efficient storage of an image without sacrificing detail. The JPEG2000 file format is one consequence of this work. Her book on the subject remains central to the body of work on wavelet theory. She has also dealt with the mathematics behind the conversion from analog to digital signaling. Raw analog input, such as sound, lacks the exactness afforded to digital signals, and Prof. Daubechies' research works to improve the degree of accuracy with which this conversion takes place. Recently she has spent time as well on developing new approaches to regularize various inverse problems with applications to geophysics, neuroscience, and finance.

Useful Links

After completing her studies in Belgium at the Vrije Universiteit Brussel with a Ph.D. in physics, Prof. Daubechies worked as a researcher at her alma mater. She moved to the U.S. in 1987 to work as MTS (member of technical staff) at AT&T Bell Labs. In 1991 Prof. Daubechies began teaching mathematics at Rutgers University, and three years later she made the move to Princeton to work in PACM as well as in the mathematics department.

Curriculum Vitae Collapse/Expand

Ingrid DAUBECHIES
Princeton University
Department of Mathematics and
Program in Applied and Computational Mathematics
Fine Hall, Washington Road
Princeton, NJ 08544-1000 USA

Date and place of birth: August 17, 1954 in Houthalen, Belgium
Citizenship: Belgian Citizen and US Naturalized Citizen, 1996

Education:
  1975 Bachelor's degree in Physics; Vrije Universiteit Brussel
  1980 Ph.D. in Physics; Vrije Universiteit Brussel
 
Positions Held:
  1975-1984 Research Assistant ("IIKW-vorser"); Department of Theoretical Physics, Vrije Universiteit Brussel
  1984-1987 Tenured Assistant Professor ("Bevoegdverklaard IIKW-vorser"); Department of Theoretical Physics, Vrije Universiteit Brussel
  1987-1994 Technical Staff Member; Mathematics Research Center, AT&T Bell Laboratories (part-time: 1/92-7/93)
  1991-1994 Full Professor; Department of Mathematics, Rutgers University (on leave from 7/93-6/94)
  1993-present Full Professor; Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University
  1997-2001 Director; Program in Applied and Computational Mathematics, Princeton University
  2005-present Full Professor; Center for the Study of Brain, Mind and Behavior, Princeton University
  2007-present Director of Graduate Studies; Program in Applied and Computational Mathematics, Princeton University
 
Awards and Honors:
  1984 Louis Empain Prize for Physics
  1992-1997 Fellow of the John D. and Catherine T. MacArthur Foundation
  1993 Elected Member of the American Academy of Arts and Sciences
  1994 American Mathematical Society Steele Prize for Exposition
  1997 American Mathematical Society Ruth Lyttle Satter Prize
  1998 The Intl Society for Optical Engineering Recognition of Outstanding Achievement
  1998 Elected Member of the National Academy of Sciences
  1998 IEEE Information Theory Society Golden Jubilee Award for Technological Innovation
  1998 Fellow of The Institute of Electrical and Electronics Engineers, Inc.
  1999 Elected Foreign Member of the Royal Netherlands Academy of Arts and Sciences
  2000 National Academy of Sciences Medal in Mathematics
  2000 Eduard Rhein Foundation 2000 Basic Research Award
  2003 Elected Member of the American Philosophical Society
  2004 William R. Kenan, Jr. Professorship at Princeton University
  2005 Gold Medal of the Royal Flemish Academy of Belgium for Science and the Arts
  2007 ICIAM (Intl Congress for Industrial and Applied Mathematics) Pioneer Prize
  2007 Honorary Member of the London Mathematical Society
  Doctor Honoris Causa
 
  2000 Université Libre de Bruxelles, Nivelles, Belgium
  2001 Ecole Polytechnique Fédérale, Lausanne, Switzerland
  2005 Université Pierre et Marie Curie, Paris, France
  2006 Università degli Studi di Genova, Genoa, Italy

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Selected Talks (last 5 years):
  • NIH Conference, Bethesda, MD (4/04) – no information
  • Mathematisches Forchunginstiut, Germany (7/04) – no information
  • Wavelets and Multifractal Analysis 2004, Institut d'Études Scientifiques de Cargèse, Corsica, France (7/04)
  • 17th Annual Conference on Learning Theory, Alberta, Canada (7/04)
  • Acivs 2004 (Advanced Concepts for Intelligent Vision Systems), Brussels, Belgium (8/04)
  • IPAM MGA Workshop V: Math Analysis and Multiscale Geometric Analysis, Los Angeles, CA (11/04)
  • AMS Josiah Willard Gibbs Lecture, AMS-MAA Joint Mathematics Meeting, Atlanta, GA (1/05)
  • CSCMM Workshops: Oversampling and Coarse Quantization for Signals (4/05); Sparse Representation in Redundant Systems (5/05), University of Maryland, College Park, MD
  • NBP Annual Conference, Bethesda, MD (4/05) – no information
  • From Quantum to Cosmos: 2004-5 NSF Lectures Explore the Physical Sciences, Arlington, VA (5/04)
  • Intl Conference on the Interactions between Wavelets and Splines, In Honor of Professor Charles K. Chui's 65th Birthday, Athens, GA (5/05)
  • Special Semester: Modern Methods of Time-Frequency Analysis, Erwin Schrödinger Institute (ESI), Vienna, Austria (6/05)
  • AWM-SIAM Sonia Kovalevsky Lecture, SIAM Annual Meeting, New Orleans, LA (7/05)
  • Samp TA’ 05 (Sampling Theory and Applications), Samsun, Turkey (7/05)
  • IPAM Workshop: Celebration of B. Engquist's 60th Birthday: Intl Forum on Multiscale Methods and Partial Differential Equations, Los Angeles, CA (8/05)
  • 20th GRETSI Symposium on Signal and Image Processing, Louvain-la-Neuve, Belgium (9/05)
  • AWM Emmy Noether Lecture and AMS-SIAM Special Session on Frames and Operator Theory in Analysis and Signal Processing, AMS-MAA Joint Mathematics Meeting, San Antonio, TX (1/06)
  • Joint HASSIP/DFG Workshop: Recent Progress in Wavelet Analysis and Frame Theory, Bremen, Germany (1/06)
  • 6th Intl Conference on Independent Component Analysis and Blind Source Separation, Charleston, SC (3/06)
  • BIMS-MSRI Workshop, Canada (3/06) – no information
  • Howard Rowlee Lecture Series, University of Nebraska, Lincoln, NE (4/06)
  • Trends in Computational Sciences Workshop, Università degli Studi di Genova, Italy (6/06)
  • Pacific Institute for the Mathematical Sciences: Sequences and Codes, Vancouver, Canada (7/06)
  • Hamilton Lecture, Royal Irish Academy, Dublin, Ireland (10/06)
  • Intl Workshop on Current Challenges in Kernel Methods 2006, Brussels, Belgium (11/06)
  • Signals, Sensors & Scheduling Workshop, University of Melbourne, Australia (12/06)
  • Special session at the Information Theory and Applications, San Diego, CA (2/07)
  • Clay Public Lectures Series, Cambridge, MA (4/07)
  • IP4AI Amsterdam Intl. Workshop on Image Processing for Artist Identification, Van Gogh Museum, Amsterdam (5/07), Museum of Modern Art, New York, NY (11/07)
  • Pacific Institute for the Mathematical Sciences: Conference on Applied Inverse Problems 2007: Theoretical and Computational Aspects, Vancouver, Canada (6/07)
  • Challenges in Theoretical and Applied Signal Processing: 50th Anniversary Celebration of Sputnik, Lausanne, Switzerland (10/07)
  • Texas A&M Learning Workshop, College Station, TX (10/07)
  • Johann Radin Lecture, Vienna, Austria (4/08)

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Professional Offices Held (last 5 years):
  2001-2003 Vice President of the American Mathematical Society
  2004-2008 Member of the Board of Trustees for the Princeton University Press
  2004 Member of Program Committee for Alfred P. Sloan Research Fellowship in Mathematics
  2004-2008 Member of Scientific Advisory Council Committee for the Mathematical Sciences Research Institute
  2004-2006 Member of Abel Committee
  2005 Member of the Committee for the 2005 NAS Award for Initiatives in Research
  2007-2010 Member of the NAS Temporary Nominating Group for Foreign Associates from Underrepresented Countries
  2007-2009 Member of the Intl Scientific Committee for the Intl Congress on Mathematical Physics
    Editorial Offices Held:
   
2003-2006 Editor-in-Chief forJournal of the American Mathematical Society
Member of Editorial Boards for the following journals:
  J of Fourier Analysis and Applications (Birkhäuser Boston)
  SIAM J on Mathematical Analysis (Society for Industrial and Applied Mathematics)
  1998-2007 J of the American Mathematical Society (American Mathematical Society)

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Graduate Students Mentored:
  • Blaise Agüera Y Arcas, PACM Graduate Student
  • Sandrine Anthoine, Ph.D. Princeton, Applied Math, 2005
  • Agis Athanassoulis, Ph.D. Princeton, Applied Math, 2007
  • Radu Balan, Ph.D. Princeton, Applied Math, 1998
  • Eugene Brevdo, Electrical Engineering Graduate Student
  • Konstantinos Drakakis, Ph.D. Princeton, Applied Math, 2003
  • Samuel Feng, PACM Graduate Student
  • Anna Gilbert, Ph.D. Princeton, Math, 1997
  • Cliona Golden, Ph.D. Princeton, Applied Math, 2005
  • Sinan Güntürk, Ph.D. Princeton, Applied Math, 2000
  • Igor Guskov, Ph.D. Princeton, Applied Math, 1999
  • Ying Huang, Ph.D. Rutgers, Mathematics, 1995
  • Shannon Huhges, Electrical Engineering Graduate Student
  • Stephane Maes, Ph.D. Université Catholique de Louvain, 1994
  • Gorkem Ozkaya, PACM Graduate Student
  • Gungor Polatkan, Electrical Engineering Graduate Student
  • Cynthia Rudin, Ph.D. Princeton, Applied Math, 2004
  • Gaurav Thakur, PACM Graduate Student
  • Philip Vetter, PACM Graduate Student
  • Rachel Ward, PACM Graduate Student
  • Hau-Tieng Wu, Mathematics Graduate Student
  • Özgur Yilmaz, Ph.D. Princeton, Applied Math, 2001
  • Jing Zou, Ph.D. Princeton, Applied Math, 2005
  • Chenwei Zhu, PACM Graduate Student
 
Postdoctoral Researchers Mentored:
 
Other Collaborators:
  • Dirk Aerts (Brussels, Belgium)
  • Francois Auger (Saint-Nazaire, France)
  • Joshua Brodie (Alphadyne, New York)
  • Robert Calderbank (Applied Math, Princeton)
  • Éric Chassande-Mottin (Nice, France)
  • Jonathan Cohen (Neuroscience, Princeton)
  • Zoran Cvetcovic (Harvard)
  • Wolfgang Dahmen (Aachen, Germany)
  • Tony Dahlen (Geophysics, Princeton)
  • Michel Defrise (Brussels, Belgium)
  • Christine De Mol (Brussels, Belgium)
  • Ron DeVore (U. South Carolina)
  • David Donoho (Stanford)
  • Björn Engquist (U. Texas, Austin)
  • Patrick Flandrin (Lyon, France)
  • Domenico Giannone (Hamburg, Germany)
  • Alex Grossman
  • Jim Haxby (Psychology, Princeton)
  • A.J.E.M. Janssen (Eindhoven, The Netherlands)
  • Tanya Khovanova (MIT)
  • John R. Klauder (U. Florida)
  • Jeff Lagarias (AT&T Labs)
  • Henry J. Landau (AT&T Labs)
  • Zeph Landau (UC Berkeley)
  • Elliott Lieb (Math, Princeton)
  • Michael Linser
  • Ben Logan (AT&T Labs)
  • Guust Nolet (Geophysics, Nice, France)
  • Thierry Paul (Paris, France)
  • Elena Pierpaoli (U. Southern California)
  • Gerlind Plenka (Duisburg, Germany)
  • Amos Ron (U. Wisconsin)
  • Rob Schapire (Computer Science, Princeton)
  • Peter Schröder (CalTech)
  • Wim Sweldens (Lucent Technologies)
  • Nguyen T. Thao (CUNY)
  • Vijay Vaishampayan (AT&T Labs)
  • Luminita Vese (UCLA)
  • Martin Vetterli (Lausanne, Switzerland)
  • Boon-Lock Yeo (Shanghai, China)

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last modified 10/01/08

Short Biography Collapse/Expand

Ingrid Daubechies received both her Bachelor's and Ph.D. degrees (in 1975 and 1980) from the Free University in Brussels, Belgium. She held a research position at the Free University until 1987. From 1987 to 1994 she was a member of the technical staff at AT&T Bell Laboratories, during which time she took leaves to spend six months (in 1990) at the University of Michigan, and two years (1991--93) at Rutgers University. She is now at the Mathematics Department and the Program in Applied and Computational Mathematics at Princeton University. Her research interests focus on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications.

In 1998 she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. The American Mathematical Society awarded her a Leroy P. Steele prize for exposition in 1994 for her book "Ten Lectures on Wavelets," as well as the 1997 Ruth Lyttle Satter Prize. From 1992 to 1997 she was a fellow of the John D. and Catherine T. MacArthur Foundation. She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Publication List Collapse/Expand

1 I. Daubechies, An application of hyperdifferential operators to holomorphic quantization, Lett. Math. Phys., 2 (6), pp. 459-469, 1978.
2 D. Aerts and I. Daubechies, About the structure-preserving maps of a quantum mechanical propositional system, Helv. Phys. Acta, 51, pp. 637-660, 1978.  
3 D. Aerts and I. Daubechies, Physical justification for using the tensor product to describe two quantum systems as one joint system, Helv. Phys. Acta, 51, pp. 661-675, 1978.
4 D. Aerts and I. Daubechies, A connection between propositional systems in Hilbert spaces and von Neumann algebras, Helv. Phys. Acta, 52, pp. 184-199, 1979.  
5 D. Aerts and I. Daubechies, A characterization of subsystems in physics, Lett. Math. Phys., 3 (1), pp. 11-17, 1979.
6 D. Aerts and I. Daubechies, A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation, Lett. Math. Phys., 3 (1), pp. 19-27, 1979.
7 I. Daubechies, Coherent states and projective representation of the linear canonical transformations, J. Math. Phys., 21 (6), pp. 1377-1389, 1980.
8 I. Daubechies and A. Grossmann, An integral transform related to quantization, J. Math. Phys., 21 (8), pp. 2080-2090, 1980.
9 I. Daubechies, On the distributions corresponding to bounded operators in the Weyl quantization, Comm. Math. Phys., 75 (3), pp. 229-238, 1980.
10 I. Daubechies, "Representation of quantum mechanical operators by kernels on Hilbert spaces of analytic functions," Ph.D. Thesis, Free University Brussels (VUB), 1980.  
11 I. Daubechies, "Weylkwantisatie bestudeerd langs de koherente toestanden om," Contest for Travelling Fellowships of the Belgian Government, 1980, (in Dutch).  
12 J.R. Klauder and I. Daubechies, Measures for path integrals, Phys. Rev. Lett., 48, pp. 117-120, 1982.
13 I. Daubechies, A. Grossmann, and J. Reignier, An integral transform related to quantization II: Some mathematical properties, J. Math. Phys., 24 (2), pp. 239-243, 1983.
14 I. Daubechies and J.R. Klauder, Constructing measures for path integrals, J. Math. Phys., 23 (10), pp. 1806-1822, 1982.
15 J.R. Klauder and I. Daubechies, "Wiener measures for quantum mechanical path integrals," in Stochastic Processes in Quantum Theory and Statistical Physics 173, S. Albeverio, Ph. Combe, and M. Sirugue-Collin (Eds.), pp. 244-247, Springer Berlin / Heidelberg, 1982.
16 I. Daubechies, Continuity statements and counterintuitive examples in connection with Weyl quantization, J. Math. Phys., 24 (6), pp. 1453-1461, 1983.
17 D. Aerts and I. Daubechies, A simple proof that the logical structure preserving map between quantum mechanical proposition systems conserves the angles, Helv. Phys. Acta, 56, pp. 1187-1190, 1983.  
18 I. Daubechies and J.R. Klauder, Measures for more quadratic path integrals, Lett. Math. Phys., 7 (3), pp. 229-234, 1983.
19 I. Daubechies and E. Lieb, One-electron relativistic molecules with Coulomb interaction, Comm. Math. Phys., 90 (4), pp. 497-510, 1983.
  Also as part of book entitled The Stability of Matter: From Atoms to Stars, Selecta of Elliott H. Lieb, Part V, W. Thirring (Ed.), Springer Berlin Heidelberg, 2005.
20 I. Daubechies, An uncertainty principle for fermions with generalized kinetic energy, Comm. Math. Phys., 90 (4), pp. 511-520, 1983.
21 I. Daubechies and E. Lieb, "Relativistic molecules with Coulomb interaction," pp. 143-148 in Proceedings of the 1983 UAB Conference on Differential Equations, eds. I. Knowles and R. Lewis, North-Holland, 1984.  
22 J.R. Klauder and I. Daubechies, Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians, Phys. Rev. Lett., 52, pp. 1161-1164, 1984.
23 I. Daubechies, One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum, Comm. Math. Phys., 94 (4), pp. 523-535, 1984.
24 I. Daubechies, "Weylkwantisatie bestudeerd via een integraaltransformatie met behulp van het koherentetoestanden-formalisme," Paper awarded the 1984 Louis Empain Prize (Belgium) for Physics, 1984, (in Dutch).  
25 I. Daubechies and J.R. Klauder, Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II, J. Math. Phys., 26 (9), pp. 2239-2256, 1985.
26 I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (5), pp. 1271-1283, 1986.
27 I. Daubechies and J.R. Klauder, "True measures for real time path integrals," pp. 425-432 in Path Integrals from meV to MeV, eds. S. Albeverio, C. Inomata, J.R. Klauder, and L. Streit, World Scientific, 1986.  
28 I. Daubechies and A. Grossmann, Frames in the Bargmann space of entire functions, Comm. Pure & Appl. Math., 41 (2), pp. 151-164, 1988.
29 I. Daubechies, J.R. Klauder, and T. Paul, Wiener measures for path integrals with affine kinematic variables, J. Math. Phys., 28 (1), pp. 85-102, 1987.
30 I. Daubechies, "Discrete sets of coherent states and their use in signal analysis," in Differential Equations and Mathematical Physics 1285, I.W. Knowles and Y. Saito (Eds.), pp. 73-82, Springer Berlin / Heidelberg, 1987.
31 I. Daubechies, Time-frequency localization operators: a geometric phase space approach, IEEE Trans. Inf. Theory, 34 (4), pp. 605-612, 1988.
32 I. Daubechies and T. Paul, "Wavelets - some applications," pp. 675-686 in Proceedings of the International Conference on Mathematical Physics, eds. M. Mebkhout and R. Seneor, World Scientific, Marseille, France, 1987.  

33

 I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inf. Theory, 36 (5), pp. 961-1005, 1990.
34 I. Daubechies and T. Paul, Time-frequency localization operators-a geometric phase space approach II. The use of dilations, Inverse Problems, 4 (3), pp. 661-680, 1988.
35 I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure & Appl. Math., 41 (7), pp. 909-996, 1988.
36 I. Daubechies, "Orthonormal bases of wavelets with finite support - connection with discrete filters," Proc. 1987 Intl. Workshop on Wavelets and Appl., Marseille, France, eds. J.M. Combes, A. Grossmann, and Ph. Tchamitchian, Springer, Berlin, 1989.  
37 I. Daubechies and A.J.E.M. Janssen, Two theorems on lattice expansions, IEEE Trans. Inf. Theory, 39 (1), pp. 3-6, 1993.
38 I. Daubechies and J.C. Lagarias, Two-scale difference equations. I. Existence and global regularity of solutions, SIAM J. Math. Anal., 22 (5), pp. 1388-1410, 1991.
39 I. Daubechies and J.C. Lagarias, Two-scale difference equations. II. Local regularity, infinite products of matrices, and fractals, SIAM J. Math. Anal., 23 (4), pp. 1031-1079, 1992.
40 I. Daubechies, "Phase space path integrals, coherent states and Wiener measure," Proceedings of the 1987-1988 Workshop on Path Integrals, Columbia University (Montreal) and Sherbrooke University, Canada, Suppl. Rendiconti Cinc. Mat. di Palermo II, 25, pp. 157-176, 1991.  
41 I. Daubechies and J.C. Lagarias, Sets of matrices all infinite products of which converge, Lin. Alg. & Appl., 161, pp. 227-263, 1992.
42 I. Daubechies, "The wavelet transform: a method for time-frequency localization," chapter 8 (pp. 366-417) in the book Advances in Spectrum Analysis and Array Processing, Vol. 1, ed. S. Haykin, Prentice-Hall, 1991.  
43 I. Daubechies, S. Jaffard, and J.L. Journé, A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal., 22 (2), pp. 554-572, 1991.
44 I. Daubechies, Orthonormal bases of compactly supported wavelets, II. Variations on a theme, SIAM J. Math. Anal., 24 (2), pp. 499-519, 1993.
45 A. Cohen and I. Daubechies, Orthonormal bases of compactly supported wavelets, III. Better frequency localization, SIAM J. Math. Anal., 24 (2), pp. 520-527, 1993.
46 M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, Image coding using wavelet transform, IEEE Trans. Image Proc., 1 (2), pp. 205-220, 1992.
47 A. Cohen, I. Daubechies, and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure & Appl. Math., 45 (5), pp. 485-560, 1992.
48 A. Cohen and I. Daubechies, Non separable bidimensional wavelet bases, Rev. Mat. Iberoamericana, 9, pp. 51-137, 1993.  
49 A. Cohen and I. Daubechies, A stability criterion for biorthogonal wavelet bases and their related subband coding scheme, Duke Math. J., 68 (2), pp. 313-335, 1992.
50 A. Cohen and I. Daubechies, On the instability of arbitrary biorthogonal wavelet packets, SIAM J. Math. Anal., 24 (5), pp. 1340-1354, 1993.
51 I. Daubechies and J.R. Klauder, "Squeezed states and path integrals," in Proc. 1991 Conf. Squeezed States, Atlanta, GA, 1991.  
52 I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Lecture Notes nr. 61, SIAM, 1992.  
53 A. Cohen, I. Daubechies, B. Jawerth, and P. Vial, Multiresolution analysis, wavelets and fast algorithms on an interval, Comptes Rendus Acad. Sci. Paris, 316 (série 1), pp. 417-421, 1993.  
54 A. Cohen, I. Daubechies, and P. Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comp. Harm. Anal., 1 (1), pp. 54-81, 1993. Tables
55 I. Daubechies, "Wavelets on the interval," pp. 95-107 in Progress in Wavelet Analysis and Applications, Y. Meyer and S. Roques (eds.), Editions Frontières, France, 1993.  
56 I. Daubechies, "Wavelets and signal analysis," paper presented at the 1992 symposium on "Frontiers of Science" organized by the National Academy of Sciences.  
57 I. Daubechies, "Wavelet transforms and orthonormal wavelet bases," pp. 1-33 in "Different perspectives on wavelets" AMS Short Course Lecture Note Series nr. 47, I. Daubechies (Ed.), AMS, 1993.  
58 I. Daubechies, "Two recent results on wavelets: wavelet bases for the interval, and biorthogonal wavelets diagonalizing the derivative operator," pp. 237-257 in Topics in Theory and Applications of Wavelets, eds. L. Schumaker and G. Webb, Academic Press, 1993.  
59 I. Daubechies, "Wavelets making waves in Mathematics and Engineering," videotape of an MAA invited lecture at the January 1992 AMS-MAA meeting in Baltimore, available in the AMS-series "Selected Lectures in Mathematics".  
60 I. Daubechies and J.C. Lagarias, On the thermodynamic formalism for multifractal functions, pp. 213-264 in The State of Matter, eds. M. Aizenman and H. Araki, dedicated to E.H. Lieb, World Scientific, 1994.
  Also published in Rev. of Math. Phys., 6 (5a), pp. 1033-1070, 1994.  
61 I. Daubechies and Y. Huang, How does truncation of the mask affect a refinable function?, Const. Approx., 11 (3), pp. 365-380, 1995.  
62 I. Daubechies, "Orthonormal bases of coherent states: the canonical case and the ax+b-group," in the Proc. Intl. Symp. Coherent States: Past, Present, and Future, pp. 103-117, eds. D.H. Feng, J.R. Klauder, and M.R. Strayer, World Scientific Publishing Co., 1994.  
63 I. Daubechies, "Ondelettes," book review in Nature, 262 (1993) pp. 1589-1591 of the books Wavelets and Operators and Wavelets: algorithms and applications, both authored by Y. Meyer.  
64 I. Daubechies and Y. Huang, A decay theorem for refinable functions, Appl. Math. Lett., 7 (4), pp. 1-4, 1994.
64a I. Daubechies, Affine coherent states and wavelets, On Klauder's path: a field trip, pp. 35--42, World Sci. Publ., River Edge, NJ, 1994.  
65 A. Cohen and I. Daubechies, A new technique to estimate the regularity of refinable functions, Rev. Mat. Iberoamericana, 12, pp. 527-591, 1996.
66 I. Daubechies, "Wavelets and other phase space localization methods," in the Proc. Intl. Congress of Mathematicians, Zürich, Switzerland, 1994, Birkhäuser Verlag, Basel Switzerland, 1995.
67 I. Daubechies, H. Landau, and Z. Landau, Gabor time-frequency lattices and the Wexler-Raz identity, J. Fourier Anal. Appl., 1 (4), pp. 437-478, 1994.
68 I. Daubechies, "Better dual functions for Gabor time-frequency lattices," in the Proc. Intl. Conf. Approximation Theory VIII, Volume 2: Wavelets and Multilevel Approximation, pp. 113-116, eds. C. Chui and L. Schumaker, World Scientific Publishing Co., 1995.
69 I. Daubechies and S. Maes, A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models, in Wavelets in Medicine and Biology, pp. 527-546, eds. A. Aldroubi and M. Unser, CRC Press, 1996 .
  Also published as "An application of a formula of Alberto Calderón to speaker identification," Harmonic analysis and partial differential equations (Chicago, IL, 1996), 163--181, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 1999.
70 A. Cohen, I. Daubechies, and G. Plonka, Regularity of refinable function vectors, J. Fourier Anal. Appl., 3, pp. 295-324, 1997.
71 I. Daubechies, "Using Fredholm determinants to estimate the smoothness of refinable functions," in the Proc. Intl. Conf. Approximation Theory VIII, Volume 2: Wavelets and Multilevel Approximation, pp. 89-112, eds. C. Chui and L. Schumaker, World Scientific Publishing Co., 1995.
72 A. Cohen, I. Daubechies, and A. Ron, How smooth is the smoothest function in a given refinable space?, Appl. Comp. Harm. Anal., 3 (1), pp. 87-89, 1996.
73 I. Daubechies and A. Gilbert, "Harmonic analysis, wavelets, and applications," lecture series presented at the Institute for Advanced Study's Park City Mathematics Institute July 1995, in the Graduate Summer School Lectures, American Mathematical Society, July 1998.  
74 I. Daubechies, "Where do wavelets come from?--A personal point of view", in Proc. IEEE, Special Issue on Wavelets, 84 (4), pp. 510-513, 1996.
75 M. Unser and I. Daubechies, On the approximation power of convolution-based least squares versus interpolation, IEEE Trans. Sig. Proc., 45 (7), pp. 1697-1711, July 1997.
75a

I. Daubechies, From the original framer to present-day time-frequency and time-scale frames, Dedicated to the memory of Richard J. Duffin. J. Fourier Anal. Appl., 3 (5), pp. 485-486, 1997.

76 A.R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo, Wavelet transforms that map integers to integers, Appl. Comp. Harm. Anal., 5 (3), pp. 332-369, 1998.
77 I. Daubechies and W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal. Appl., 4 (3), pp. 247-269, 1998 .
  Also as part of book entitled Wavelets in the Geosciences 90, R. Klees and R. Haagmans (Eds.), Springer Berlin / Heidelberg, 2000.
78 E. Chassande-Mottin, I. Daubechies, F. Auger and P. Flandrin, Differential reassignment, IEEE Sig. Proc. Lett., 4 (10), pp. 293-294, 1997.
79 F. Auger, E. Chassande-Mottin, I. Daubechies and P. Flandrin, "Partition du Plan Temps-Fréquence et réallocation" in the Proceedings of the Seizième Colloque Gretsi sur le Traitement du Signal et des Images, pp. 1447-1450, Grenoble (France), September 1997.  
80 I. Daubechies, I. Guskov, and W. Sweldens, Regularity of irregular subdivision, Const. Approx., 15 (3), pp. 381-426, 1999.
81 A. Cohen, I. Daubechies, O. Guleryuz and M. Orchard, On the importance of combining non-linear approximation with coding strategies, IEEE Trans. Inf. Theory, 48 (7), pp. 1895-1921, 2002.
82 A.R. Calderbank, I. Daubechies, W. Sweldens and B.-L. Yeo, "Lossless image compression using integer to integer wavelet transforms," in Proc. Int. Conf. Image Proc., Santa Barbara, CA, Oct 1997, vol.1, pp. 596-599, 1997.
83 I. Daubechies, Recent results in wavelet applications, J. Electronic Imaging, 7 (4), pp. 719-724, 1998 .
  Also as part of book entitled Wavelet Applications V, H. Szu (ed.), Proc. SPIE vol. 3391, pp. 2-9, 1998.
84 A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore, Tree approximation and optimal encoding, Appl. Comp. Harm. Anal., 11 (2), pp. 192-226, 2001.
85 D.L. Donoho, M. Vetterli, R.A. DeVore, I. Daubechies, Data compression and harmonic analysis, IEEE Trans. Inf. Theory, 44 (6), pp. 2435-2476, 1998.
86 I. Daubechies, I. Guskov, P. Schröder, and W. Sweldens, Wavelets on Irregular Point Sets, Phil. Trans R. Soc. A, 357 (1760), pp. 2397-2413, 1999 .
  Also as part of book entitled Wavelets: The Key to Intermittent Information?, B.W. Silverman and J.C. Vassilicos (Eds.), Oxford Univ. Press, USA, 2000.  
87 R.V. Balan, I. Daubechies, and V. Vaishampayan, The Analysis and Design of Windowed Fourier Frame based Multiple Description Source Coding Schemes, IEEE Trans. Inf. Theory, 46 (7), pp. 2491-2536, 2000.
88 Z. Cvetkovic, I. Daubechies, Single-bit oversampled A/D conversion with exponential accuracy in the bit-rate, in Proc. Data Compression Conference (DCC) 2000, Snowbird, UT, Mar 2000, pp. 343-352, 2000.
89 A.R. Calderbank and I. Daubechies, The Pros and Cons of Democracy, IEEE Trans. Inf. Theory, 48 (6), pp.1721-1725, 2002.
90 I. Daubechies, I. Guskov and W. Sweldens, Commutation for Irregular Subdivision, Const. Approx., 17 (4), pp. 479 - 514, 2001.
91 I. Daubechies and R. DeVore, Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order, Annals of Math., 158 (2), pp.679-710, 2003.
92 I. Daubechies and B. Han, Pairs of Dual Wavelet Frames From Any Two Refinable Functions, Const. Approx., 20 (3), pp. 325-352, 2004.
93 I. Daubechies and B. Han, The Canonical Dual Frame of a Wavelet Frame, Appl. Comp. Harm. Anal., 12 (3), pp. 269-285, 2002.
94 A. Cohen, W. Dahmen, I. Daubechies and R. DeVore, Harmonic analysis of the space BV, Rev. Mat. Iberoamericana, 19, pp. 235-262, 2003.
95 I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-Based constructions of Wavelet Frames, Appl. Comp. Harm. Anal., 14 (1), pp. 1-46, 2003.
96 I. Daubechies, O. Runborg and W. Sweldens, Normal Multiresolution Approximation of Curves, Const. Approx., 20 (3), pp. 399-463, 2004.
97 R.V. Balan and I. Daubechies, Optimal Stochastic Encoding and Approximation Schemes Using Weyl-Heisenberg Sets, in Advances in Gabor Analysis, H.G. Feichtinger and T. Strohmer (Eds.), Birkhaeuser, Boston, pp. 259-320, 2003.
98 I. Daubechies and F. Planchon, Adaptive Gabor Transforms, Appl. Comp. Harm. Anal., 13 (1), pp. 1-21, 2002.
99 I. Daubechies, R. DeVore, C.S. Güntürk and V.A. Vaishampayan, "Beta Expansions: A New Approach to Digitally Correct A/D Conversion", in Proc. IEEE Int. Symp. Circuits and Systems (ISCAS) 2002, Phoenix, AZ, May 2002, vol.2, pp. II-784 - II-787, 2002.
100 I. Daubechies, R. DeVore, C.S. Güntürk and V.A. Vaishampayan, A/D Conversion with Imperfect Quantizers, IEEE Trans. Inf. Theory, 52 (3), pp. 874-885, 2006.
101 I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math, 57 (11), pp.1413-1457, 2004.
102 Z. Cvetkovic, I. Daubechies and B. Logan, Single-Bit Oversampled A/D Conversion with Exponential Accuracy in the Bit-Rate, IEEE Trans. Inf. Theory, 53 (11), pp. 3979-3989, 2007.
103 C. Rudin, I. Daubechies and R. Schapire, "On the Dynamics of Boosting," in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, B. Schölkopf (Eds.), MIT Press, Cambridge, MA, 2004.
104 C. Rudin, R. E. Schapire and I. Daubechies "Boosting Based on a Smooth Margin," in Learning Theory 3120, J. Shawe-Taylor Y. Singer (Eds.), pp. 502-517, Springer Berlin / Heidelberg, 2004.
105 I. Daubechies and G. Teschke, Varitional image restoration by means of wavelets: simultaneous decomposition, deblurring and denoising, Appl. Comp. Harm. Anal., 19 (1), pp. 1-16, 2005.
106 C. Rudin, I. Daubechies and R. E. Schapire, The Dynamics of AdaBoost: Cyclic Behavior and Convergence of Margins, J. Machine Learning Research, 5 (Dec), pp. 1557-1595, 2004.
107 C. Rudin, R. E. Schapire and I. Daubechies, Analysis of Boosting Algorithms using the Smooth Margin Function, Annals of Statistics, 35 (6), pp. 2723-2768, 2007.
108 I. Daubechies, K. Drakakis and T. Kovanova, A detailed study of the Attachment Strategies of New Autonomous Systems in the AS Connectivity Graph, Internet Mathematics, 2 (2), pp. 185-246, 2005.
109 J. Zou, A. Gilbert, M. Strauss and I. Daubechies, Theoretical and Experimental Analysis of a Randomized Algorithm for Sparse Fourier Transform Analysis, J. Comp. Physics, 211 (2), pp. 572-595, 2006.
110 S. Takerkart, M. Benharrosh, J. Haxby and I. Daubechies, Estimating spatially distributed patterns of brain activity in fMRI datasets by using ICA, to appear in NeuroImage.  
111 E. Pierpaoli, S. Anthoine, K. Huffenberger and I. Daubechies, Reconstructing Sunyaev-Zeldovich clusters in future CMB experiments, Mon. Not. R. Astron. Soc. 359 (1), pp. 261-271, May 2005.
112 I. Daubechies, "Correction d'erreurs et compression", Mathématique et Pédagogie, No. 157, pp. 5-33, 2006.  
113 S.M. Hughes and I. Daubechies, Simpler Alternatives to Information Theoretic Similarity Metrics for Multimodal Image Alignment, Proc. 2006 IEEE Intl. Conf. Image Proc., 8-11 Oct. 2006, pp. 365-368, 2006.
114 I. Daubechies and Ö. Yilmaz, Robust and practical analog-to-digital conversion with exponential precision, IEEE Trans. Inform. Theory, 52 (8), pp. 3533-3545, 2006.
115 I. Daubechies, G. Teschke and L. Vese, Iteratively solving linear inverse problems under general convex constraints, Inverse Probl. Imaging, 1 (1), pp. 29-46, 2007.
116 I. Daubechies, O. Runborg and J. Zou, A sparse spectral method for homogenization multiscale problems, Multiscale Model. Simul. 6 (3), pp. 711-740, 2007.
117 C. Rudin, R.E. Schapire and I. Daubechies, Precise Statements of Convergence for AdaBoost and arc-gv, Contemp. Math., 443, pp. 131-145, 2007; AMS-IMS-SIAM Joint Summer Research Conf. on Machine and Statistical Learning, Prediction and Discovery, 2007.
118 I. Loris, G. Nolet, I. Daubechies and F.A. Dahlen, Tomographic inversion using $\ell_1$-norm regularization of wavelet coefficients, Geophysical J. Intl., 170 (1), pp. 359-370, 2007.
119 I. Daubechies, M. Fornasier and I. Loris, Accelerated projected gradient method for linear inverse problems with sparsity constraints, J. Fourier anal. appl., to appear.
120 I. Daubechies, Wavelets and Applications, to appear in A Princeton Companion to Mathematics, T. Gowers (ed.), Princeton University Press, 2008.
121 I. Daubechies, G. Teschke and L. Vese, On Some Iterative Concepts for Image Restoration, to appear in Multi-volume book: Advances in Imaging and Electron Physics, Peter Hawkes (ed.), 150, 2008.
122 C. R. Johnson, Jr., E. Hendriks, I. Berezhnoy, E. Brevdo, S. Hughes, I. Daubechies, J. Li, E. Postma and J. Wang, Image Processing for Artist Identification: Brushwork in the Paintings of Vincent Van Gogh, Signal Processing Mag., to appear.  
123 J. Brodie, I. Daubechies, C. De Mol and D. Giannone, Sparse and stable Markowitz portfolios, 2007.
124 I. Daubechies, E. Roussos, S. Takerkart, M. Benharrosh, C. Golden, K. D'Ardenne, W. Richter, J. D. Cohen and J. Haxby, Independent component analysis for brain fMRI does not select for independence, P NATL ACAD SCI USA, 106, pp. 10415-10422, 2009 .

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Parlez-vous Wavelets? Interview of Ingrid Daubechies in What's Happening in Mathematical Sciences

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2007 ICIAM Pioneer Prize
2005 Gold Medal (Gouden Penning) of the Flemish Royal Academy of Arts and Sciences
2000 Eduard Rhein Foundation Basic Research Award
2000 National Academy of Sciences Medal in Mathematics
1992 MacArthur Fellowship

Professor Daubechies holds a joint appointment with PACM and the department of mathematics. From 1997-2001 she served as the director of PACM. She is responsible for the direction of the mathematics part of the integrated engineering sequence available to freshmen intending to major in engineering, and she teaches an undergraduate introductory course in applied mathematics.

PACM Students advised: S. Anthoine, A. Athanassoulis, R. Balan, K. Drakakis, S. Feng, C. Golden, S. Güntürk, I. Guskov, G. Ozkaya, C. Rudin, G. Thakur, P. Vetter, R. Ward, Ö. Yilmaz, J. Zou, C. Zhu

Affiliations:
Applied & Computational Mathematics
Mathematics

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