Ingrid Daubechies' Publication List

All "papers" (including various book chapters, a book, and a video) are listed in the chronological order of their creation. Boldface titles indicate original research results published or to be published in, or submitted to, refereed research journals or books. The other titles contain these same results in a different form (Ph.D. thesis, book, review articles, conference proceedings, ...).

Some papers are available in .PS format

  1. I. Daubechies, An application of hyperdifferential operators to holomorphic quantization, Lett. Math. Phys. 2, 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, 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, pp. 19--27, 1979.

  7. I. Daubechies, Coherent states and projective representation of linear canonical transformations, J. Math. Phys. 21, pp. 1377--1388, 1980.

  8. I. Daubechies and A. Grossmann, An integral transform related to quantization, J. Math. Phys. 21, pp. 2080--2090, 1980.

  9. I. Daubechies, On the distributions corresponding to bounded operators in the Weyl quantization, Comm. Math. Phys. 75, 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. 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, pp. 239--243, 1983.

  14. I. Daubechies and J. Klauder, Constructing measures for path integrals, J. Math. Phys. 23, pp. 1806--1822, 1982.

  15. J. Klauder and I. Daubechies, "Wiener measures for quantum mechanical path integrals," Lecture Notes in Physics 173, pp. 244--247, Springer-Verlag, 1982.

  16. I. Daubechies, Continuity statements and counterintuitive examples in connection with Weyl quantization, J. Math. Phys. 24, 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. Klauder, Measures for more quadratic path integrals, Lett. Math. Phys. 7, pp. 229--234, 1983.

  19. I. Daubechies and E. Lieb, One electron relativistic molecules with Coulomb interaction, Comm. Math. Phys. 90, pp. 497--510, 1983.

  20. I. Daubechies, An uncertainty principle for fermions with generalized kinetic energy operator, Comm. Math. Phys. 90, 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. 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, 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. Klauder, Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians II, J. Math. Phys. 26, pp. 2239--2256, 1985.

  26. I. Daubechies, A. Grossmann, and Y. Meyer, Painless non-orthogonal expansions, J. Math. Phys. 27, pp. 1271--1283, 1986.

  27. I. Daubechies and J. 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, pp. 151--164, 1988.

  29. I. Daubechies, J. Klauder, and T. Paul, Wiener measures for path integrals with affine kinematic variables, J. Math. Phys. 28, pp. 85--102, 1987.

  30. I. Daubechies, "Discrete sets of coherent states and their use in signal analysis," pp. 73--82 in Proceedings of the 1986 International Conference on Differential Equations and Mathematical Physics, Birmingham, Alabama, eds. I.W. Knowles and Y. Saito, Springer, 1987.

  31. I. Daubechies, Time-frequency localization operators: A geometric phase space approach, IEEE Trans. on Inf. Theory 34, 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, pp. 961--1005, 1990.

  34. I. Daubechies and T. Paul, Time-frequency localization operators: A geometric phase space approach II. The use of dilations and translations, Inverse Problems 4, pp. 661--680, 1988.

  35. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure & Appl. Math. 41, pp. 909--996, 1988.

  36. I. Daubechies, "Orthonormal bases of wavelets with finite support -- connection with discrete filters," Proceedings of the 1987 International Workshop on Wavelets and Applications, 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, 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, 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, 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, pp. 554--572, 1991.

  44. I. Daubechies, Orthonormal bases of compactly supported wavelets, II. Variations on a theme, SIAM J. Math. Anal. 24, 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, pp. 520--527, 1993.

  46. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, Image coding using the wavelet transform, IEEE Trans. Image Proc. 1, pp. 205--220, 1992.

  47. A. Cohen, I. Daubechies, and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure & Appl. Math 45, 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, pp. 313--335, 1992.

  50. A. Cohen and I. Daubechies, On the instability of arbitrary biorthogonal wavelet packets, SIAM J. Math. Anal. 24, pp. 1340--1354, 1993.

  51. I. Daubechies and J.R. Klauder, "Squeezed states and path integrals," in Proceedings of the 1991 Conference on Squeezed States, Atlanta, Georgia.

  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, Applied and Computational Harmonic Analysis 1, pp. 54--81, 1993.
     
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  55. I. Daubechies, "Wavelets on the interval," pp. 95--107 in Progress in Wavelet Analysis and Applications, eds. Y. Meyer and S. Roques, 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, ed. I. Daubechies, 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. 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 Reviews of Mathematical Physics 6, pp. 1033--1070, 1994.

  61. I. Daubechies and Y. Huang, How does truncation of the mask affect a refinable function?, Constructive Approximation 11, pp. 365--380, 1995.

  62. I. Daubechies, "Orthonormal bases of coherent states: the canonical case and the ax+b-group," in the Proceedings of the International Symposium 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, Applied Mathematics Letters 7, pp. 1--4, 1994.

  65. A. Cohen and I. Daubechies, A new technique to estimate the regularity of refinable functions, Revista Matematica Iberoamericana, 12, pp. 527--591, 1996.

  66. I. Daubechies, "Wavelets and other phase space localization methods," in the Proceedings of the International 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, Journal of Fourier Analysis and Applications 1, pp. 437--478, 1995.

  68. I. Daubechies, "Better dual functions for Gabor time-frequency lattices," in the Proceedings of the International Conference 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.

  70. A. Cohen, I. Daubechies, and G. Plonka, Regularity of refinable function vectors, Journal of Fourier Analysis and Applications 3, pp. 295--324, 1997.

  71. I. Daubechies, "Using Fredholm determinants to estimate the smoothness of refinable functions," in the Proceedings of the International Conference 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?, Applied and Computational Harmonics Analysis 3, 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, to appear 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 the Proceedings of the IEEE Special Issue on Wavelets 84 (no. 4), pp. 510--513, April 1996.

  75. M. Unser and I. Daubechies, On the approximation power of convolution-based least squares versus interpolation, IEEE Trans. Sig. Proc., 45 (no. 7), pp. 1697--1711, July 1997.

  76. A.R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo, Wavelet transforms that map integers to integers, Applied and Computational Harmonics Analysis 5 (no. 3), pp. 332--369, 1998.

  77. I. Daubechies and W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal. Appl., 4 (no. 3), pp. 247-269, 1998.

  78. F. Auger, E. Chassande-Mottin, I. Daubechies and P. Flandrin, Differential reassignment, IEEE Signal Proc. Letters, 4 (no. 10), pp. 293-294, October 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, Constructive Approximation, 15 (no. 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 Transactions in Information Theory, 48, 2002.

  82. A.R. Calderbank, I. Daubechies, W. Sweldens and B.-L. Yeo, "Lossless image compression using integer to integer wavelet transforms," in the Proceedings of the International Conference on Image Processing, Vol. I, pp. 596-599, October 1997.

  83. I. Daubechies, "Recent results in wavelet applications," Journal of Electronic Imaging, 7 (no. 4), pp. 719-724, 1998.

  84. A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore, Tree approximation and optimal encoding Applied and Computational Harmonic Analysis , 11, 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 (no. 6), pp. 2435-2476, 1998.

  86. I. Daubechies, I. Guskov, P. Schröder, and W. Sweldens, Wavelets on Irregular Point Sets, Phil. Trans. R. Soc. Lon. A., 357 (no. 1760), pp. 2397-2413, 1999. Also as part of book entitled Wavelets: The Key to Intermittent Information, edited by B.W. Silverman and J.C. Vassilicos, September 2000.

  87. R. Balan, I. Daubechies, and V. Vaishampayan, The Analysis and Design of Windowed Fourier Frame based Multiple Description Source Coding Schemes, IEEE Trans. on Info. Th. 46 (no. 7), pp. 2491-2536, 2000.

  88. Z. Cvetkovic and I. Daubechies, Single-Bit Oversampled A/D Conversion with Exponential Accuracy in the Bit-Rate, Conference Proceedings of DCC 2000.

  89. A.R. Calderbank and I. Daubechies, The Pros and Cons of Democracy, IEEE Transactions in Information Thoery, January 2003.

  90. I. Daubechies, I. Guskov and W. Sweldens, Commutation for Irregular Subdivision, Constructive Approximation 15, pp. 381-426, 2001.

  91. I. Daubechies and R. DeVore, Reconstructing a bandlimited function from very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order, Annals of Mathematics 158, pp.670-710, 2003.

  92. I. Daubechies and B. Han, Pairs of Dual Wavelet Frames From Any Two Refinable Functions, to appear in Constructive Approximation.

  93. I. Daubechies and B. Han, The Canonical Dual Frame of a Wavelet Frame, Applied and Computational Harmonics Analysis, 12, pp. 269-285, 2002.

  94. A. Cohen, W. Dahmen, I. Daubechies and R. DeVore, Harmonic analysis of the space BV, Revista Matematica Iberoamericana 19, pp. 235-262, 2003.

  95. I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-Based constructions of Wavelet Frames Applied and Computational Harmonics Analysis 14, pp. 1-46, 2003.

  96. I. Daubechies, O. Runborg and W. Sweldens, Normal Polyline Approximation, to appear in Constructive Approximation.

  97. R.V. Balan and I. Daubechies, Optimal Stochastic Encoding and Approximation Schemes Using Weyl-Heisenberg Sets, Advances in Gabor Analysis, H.G. Feichtinger and T. Strohmer editors, Birkhaeuser, Boston, pp. 259 - 320, 2003.

  98. I. Daubechies and F. Planchon, Adaptive Gabor Transforms, to appear in Applied and Computational Harmonic Analysis.

  99. I. Daubechies, R. DeVore, C.S. Güntürk and V.A. Vaishampayan, Beta Expansions: A New Approach to Digitally Correct A/D Conversion, Proceedings of the IEEE International Symposium on Circuits and Systems ISCAS'2002, Phoenix, May 2002.

  100. I. Daubechies, R. DeVore, C.S. Güntürk and V.A. Vaishampayan, Exponential Precision in A/D Conversion with an Imperfect Quantizer, submitted to IEEE Journal in Information Theory (original submission August 2001, revised version after review October 2003).

  101. I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, submitted for publication.