Fundamental Papers in Wavelet Theory

Contributor Affiliations ix
Preface: Christopher Heil and David F. Walnut xiii
Acknowledgments xiv
Foreword: Ingrid Daubechies xv
Introduction: John J. Benedetto 1

Section I. Precursors in Signal Processing

Introduction: Jelena Kovacevíc 23
1.Peter J. Burt and Edward H. Adelson, The Laplacian pyramid as a compact
image code, IEEE Trans. Commun., 31 (1983), 532-540. 28
2.R. E. Crochiere, S. A. Webber, and J. L. Flanagan, Digital coding of speech in sub-bands, Bell System Technical J., 55 (1976), 1069-1085. 37
3.D. Esteban and C. Galand, Application of quadrature mirror filters to split-band voice coding schemes, ICASSP'77, IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing, 2, April 1977, 191-195. 54
4.M.J.T. Smith and T. P. Barnwell III, A procedure for designing exact reconstruction filter banks for tree-structured subband coders, ICASSP'84, IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing, 9, March 1984, 421-424. 59
5.Fred Mintzer, Filters for distortion-free two-band multirate filter banks, IEEE Trans. Acoust., Speech, and Signal Proc., 33 (1985), 626-630. 63
6.Martin Vetterli, Filter banks allowing perfect reconstruction, Signal Processing, 10 (1986), 219-244. 68
7.P. P. Vaidyanathan, Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property, IEEE Trans. Acoust., Speech, and Signal Proc., 35 (1987), 476-492. 94

Section II. Precursors in Physics: Affine Coherent States

Introduction: Jean-Pierre Antoine 113
1.Erik W. Aslaksen and John R. Klauder, Continuous representation theory using the affine group, J. Math. Physics, 10 (1969), 2267-2275. 117
2.A. Grossmann, and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., 15 (1984), 723-736. 126
3.A. Grossmann, J. Morlet, and T. Paul, Transforms associated to square integrable group representations I, J. Math. Physics, 26 (1985), 2473-2479. 140

Section III. Precursors in Mathematics: Early Wavelet Bases

Introduction: Hans G. Feichtinger 149
1.Alfred Haar, Zur Theorie der orthogonalen Funktionensysteme [On the theory of orthogonal function systems], Mathematische Annalen, 69 (1910), 331-371.
Translated by Georg Zimmermann. 155
2.Philip Franklin, A set of continuous orthogonal functions, Mathematische Annalen, 100 (1928), 522-529. 189
3.Jan-Olov Strömberg, A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces, Conf. on Harmonic Analysis in Honor of A. Zygmund, Vol. II, W. Beckner et al., eds., Wadsworth (Belmont, CA), (1983), 475-494. 197
4.Yves Meyer, Principe d'incertitude, bases hilbertiennes et algebres d'operateurs [Uncertainty principle, Hilbert bases, and algebras of operators], Seminaire Bourbaki, 1985/86. Asterisque No. 145-146 (1987), 209-223. Translated by John Horvath. 216
5.P. G. Lemaríe and Y. Meyer, Ondelettes et bases hilbertiennes [Wavelets and Hilbert bases], Revista Matematica Iberoamericana, 2 (1986), 1-18. Translated by John Horvath. 229
6.Guy Battle, A block spin construction of ondelettes I, Comm. Math. Physics, 110 (1987), 601-615. 245

Section IV. Precursors and Development in Mathematics: Atom and Frame Decompositions Introduction: Yves Meyer 263

1.R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), 341-365. 269
2.Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 83 (1977), 569-645. 295
3.Ingrid Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Physics, 27 (1986), 1271-1283. 372
4.Michael Frazier and Björn Jawerth, Decompositions of Besov spaces, Indiana Univ. Math. J., 34 (1985), 777-799. 385
5.Hans G. Feichtinger and K. H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions I, J. Funct. Anal., 86 (1989), 307-340. 408
6.Ingrid Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 39 (1990), 961-1005. 442

Section V. Multiresolution Analysis

Introduction: Guido Weiss 489
1.Stephane G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Machine Intell., 11 (1989), 674-693. 494
2.Yves Meyer, Wavelets with compact support, Zygmund Lectures, U. Chicago (1987). 514
3.Stephane G. Mallat, Multiresolution approximations and wavelet orthonormal bases for L2(R), Trans. Amer. Math. Soc., 315 (1989), 69-87. 524
4.A. Cohen, Ondelettes, analysis multirésolutions et filtres mirroirs en quadrature [Wavelets, multiresolution analysis, and quadrature mirror filters], Ann. Inst. H. Poincaré, Anal. Non Linéaire, 7 (1990), 439-459. Translated by Robert D. Ryan. 543
5.Wayne M. Lawton, Tight frames of compactly supported affine wavelets, J. Math. Phys., 31 (1990), 1898-1901. 560
6.Ingrid Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41 (1988), 909-996. 564

Section VI. Multidimensional Wavelets

Introduction: Guido Weiss 655
1.Yves Meyer, Ondelettes, fonctions splines et analyses graduées [Wavelets, spline functions, and multiresolution analysis], Rend. Sem. Mat. Univ. Politec. Torino, 45 (1987), 1-42. Translated by John Horvath. 659
2.Karlheinz Gröchenig, Analyse multi-échelle et bases d'ondelettes [Multiscale analyses and wavelet bases], C. R. Acad. Sci. Paris Série I, 305 (1987), 13-17. Translated by Robert D. Ryan. 690
3.Jelena Kovacevic and Martin Vetterli, Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn, IEEE Trans. Inform. Theory, 38 (1992), 533-555. 694
4.K. Gröchenig and W. R. Madych, Multiresolution analysis, Haar bases and self-similar tilings of Rn, IEEE Trans. Inform. Theory, 38 (1992), 556-568. 717

Section VII. Selected Applications

Introduction: Mladen Victor Wickerhauser 733
1.G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms, I, Comm. Pure Appl. Math., 44 (1991), 141-183. 741
2.Ronald A. DeVore, Björn Jawerth, Vasil Popov, Compression of wavelet decompositions, Amer. J. Math., 114 (1992), 737-785. 784
3.David L. Donoho and Iain M. Johnstone, Adapting to unknown smoothness by wavelet shrinkage, J. Amer. Statist. Assoc., 90 (1995), 1200-1224. 833
4.Stéphane Jaffard, Exposants de Hölder en des points donné et coéfficients d'ondelettes [Hölder exponents at given points and wavelet coefficients], C. R. Acad. Sci. Paris Série I, 308 (1989), 79-81. Translated by Robert D. Ryan. 858
5.Jerome M. Shapiro, Embedded image coding using zerotrees of wavelet coefficients, IEEE Trans. Signal Processing, 41 (1993), 3445-3462. 861