20 October 2010

Wavelet Theory

Last update: 27.X.2010

Precursors in Signal Processing

Author: Peter J. Burt and Edward H. Adelson
Title: The Laplacian pyramid as a compact image code
Language: English
Format: pdf
Source: CiteSeerX - IEEE Trans. Commun., 31 (1983), 532–540.

Author: R. E. Crochiere, S. A. Webber, and J. L. Flanagan
Title: Digital coding of speech in subbands
Language:
Format:
Source: ??? - Bell System Technical J., 55 (1976), 1069–1085.

Author: D. Esteban and C. Galand
Title: Application of quadrature mirror filters to split-band voice coding schemes
Language:
Format:
Source: ??? - ICASSP ’77, IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing, 2, April 1977, 191–195.

Author: M. J. T. Smith and T. P. Barnwell III
Title: A procedure for designing exact reconstruction filter banks for tree structured subband coders
Language:
Format:
Source: ??? - ICASSP ’84, IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing, 9, March 1984, 421–424.

Author: Fred Mintzer
Title: Filters for distortion-free two-band multirate filter banks
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Format:
Source: ??? - IEEE Trans. Acoust., Speech, and Signal Proc., 33 (1985), 626–630.

Author: Martin Vetterli
Title: Filter banks allowing perfect reconstruction
Language: English
Format: pdf
Source: Infoscience - Signal Processing, 10 (1986), 219–244.

Author: P. P. Vaidyanathan
Title: Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M , having the perfect reconstruction property
Language:
Format:
Source: ??? - IEEE Trans. Acoust., Speech, and Signal Proc., 35 (1987), 476–492.

Precursors in Physics: Affine Coherent States

Author: Erik W. Aslaksen and John R. Klauder
Title: Continuous representation theory using the affine group
Language:
Format:
Source: ??? - J. Math. Physics, 10 (1969), 2267–2275.

Author: A. Grossmann, and J. Morlet
Title: Decomposition of Hardy functions into square integrable wavelets of constant shape
Language: English
Format: pdf
Source: Universität Wien - SIAM J. Math. Anal. 15 (1984), 723–736.

Author: A. Grossmann, J. Morlet, and T. Paul
Title: Transforms associated to square integrable group representations I
Language: English
Format: pdf
Source: Numdam - J. Math. Physics, 26 (1985), 2473–2479.

Precursors in Mathematics: Early Wavelet Bases

Author: Alfred Haar
Title: Zur Theorie der orthogonalen Funktionensysteme [On the theory of orthogonal function systems]
Language: German, English
Format: pdf
Source: Springerlink - German: Mathematische Annalen, 69 (1910), 331–371. Translated by Georg Zimmermann.
Source: Laurent Duval - English

Author: Philip Franklin
Title: A set of continuous orthogonal functions
Language: English
Format: pdf
Source: Springerlink - Mathematische Annalen, 100 (1928), 522–529.

Author: Jan-Olov Strömberg
Title: A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces
Language:
Format:
Source: ??? - Conf. on Harmonic Analysis in Honor of A. Zygmund, Vol. II, W. Beckner et al., eds., Wadsworth (Belmont, CA), (1983), 475–494.

Author: Yves Meyer
Title: Principe d’incertitude, bases hilbertiennes et algebres d’operateurs [Uncertainty principle, Hilbert bases, and algebras of operators]
Language: French
Format: pdf
Source: Numdam - Seminaire Bourbaki, 1985/86. Asterisque No. 145-146 (1987), 209–223.

Author: P. G. Lemari ́ and Y. Meyer
Title: Ondelettes et bases hilbertiennes [Wavelets and Hilbert bases]
Language:
Format:
Source: ??? - Revista Matematica Iberoamericana, 2 (1986), 1–18. Translated by John Horváth.

Author: Guy Battle
Title: A block spin construction of ondelettes I
Language: English
Format: pdf
Source: SpringerLink - Communications in Math. Physics, 110 (1987), 601–615.
Source part II: SpringerLink


Precursors and Development in Mathematics: Atom and Frame Decompositions


Author: R. J. Duffin and A. C. Schaeffer
Title: A class of nonharmonic Fourier series
Language: English
Format: pdf
Source: Tel Aviv University - Trans. Amer. Math. Soc., 72 (1952), 341–365.

Author: Ronald R. Coifman and Guido Weiss
Title: Extensions of Hardy spaces and their use in analysis
Language: English
Format: pdf
Source: American Mathematical Society - Bull. Amer. Math. Soc., 83 (1977), 569–645.

Author: Ingrid Daubechies, A. Grossmann, and Y. Meyer
Title: Painless nonorthogonal expansions
Language:
Format:
Source: ??? - J. Math. Physics, 27 (1986), 1271–1283.

Author: Michael Frazier and Björn Jawerth
Title: Decompositions of Besov spaces
Language:
Format:
Source: ??? - Indiana Univ. Math. J., 34 (1985), 777–799.

Author: Hans G. Feichtinger and K. H. Gröchenig
Title: Banach spaces related to integrable group representations and their atomic decompositions I
Language: English
Format: pdf
Source: Universität Wien - J. Funct. Anal., 86 (1989), 307–340.
Source part II: Universität Wien

Author: Ingrid Daubechies
Title: The wavelet transform, time-frequency localization and signal analysis
Language:
Format:
Source: ??? - IEEE Trans. Inform. Theory, 39 (1990), 961–1005.

Multiresolution Analysis

Author: Stephane G. Mallat
Title: A theory for multiresolution signal decomposition: The wavelet representation
Language:
Format: pdf, ps
Source 1: Gloria Menegaz @ Università degli Studi di Siena- IEEE Trans. Pattern Anal. Machine Intell., 11 (1989), 674–693.
Source 2: New York University

Author: Yves Meyer
Title: Wavelets with compact support
Language:
Format:
Source: ??? - Zygmund Lectures, U. Chicago (1987).

Author: Stephane G. Mallat
Title: Multiresolution approximations and wavelet orthonormal bases for L2(R)
Language:
Format:
Source: Centre de Mathématiques Appliquées de l'Ecole Polytechnique - Trans. Amer. Math. Soc., 315 (1989), 69–87.

Author: A. Cohen
Title: Ondelettes, analyses multirésolutions et filtres miroirs en quadrature [Wavelets, multiresolution analysis, and quadrature mirror filters]
Language: French
Format: pdf
Source: Numdam - Ann. Inst. H. Poincar ́, Anal. Non Lin ́aire, 7 (1990), 439–459. Translated by Robert D. Ryan

Author: Wayne M. Lawton
Title: Tight frames of compactly supported affine wavelets
Language:
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Source: ??? - J. Math. Phys., 31 (1990), 1898–1901.

Author: Ingrid Daubechies
Title: Orthonormal bases of compactly supported wavelets
Language:
Format:
Source: ??? - Comm. Pure Appl. Math., 41 (1988), 909–996.

Multidimensional Wavelets

Author: Yves Meyer
Title: Ondelettes, fonctions splines et analyses graduées [Wavelets, spline functions, and multiresolution analysis]
Language: French
Format: pdf
Source: Università e Politecnico di Torino - Rend. Sem. Mat. Univ. Politec. Torino, 45 (1987), 1–42. Translated by John Horváth

Author: Karlheinz Gröchenig
Title: Analyse multi-échelle et bases d’ondelettes [Multiscale analyses and wavelet bases]
Language:
Format:
Source: ??? - C. R. Acad. Sci. Paris Série I, 305 (1987), 13–17. Translated by Robert D. Ryan.

Author: Jelena Kovačevič and Martin Vetterli
Title: Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn
Language:
Format:
Source: ??? - IEEE Trans. Inform. Theory, 38 (1992), 533–555.

Author: K. Gröchenig and W. R. Madych
Title: Multiresolution analysis, Haar bases and self-similar tilings of Rn
Language:
Format:
Source: ??? - IEEE Trans. Inform. Theory, 38 (1992), 556–568.

Applications

Author: G. Beylkin, R. Coifman, and V. Rokhlin
Title: Fast wavelet transforms and numerical algorithms, I
Language:
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Source 1: University of Colorado at Boulder - Comm. Pure Appl. Math., 44 (1991), 141–183.
Source 2: University of Michigan
Source 3: California Institute of Technology

Author: Ronald A. DeVore, Björn Jawerth, Vasil Popov
Title: Compression of wavelet decompositions
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Format:
Source: ??? - Amer. J. Math., 114 (1992), 737–785.

Author: David L. Donoho and Iain M. Johnstone
Title: Adapting to unknown smoothness by wavelet shrinkage
Language:
Format:
Source: ??? - J. Amer. Statist. Assoc., 90 (1995), 1200–1224.

Author: Stéphane Jaffard
Title: Exposants de Hölder en des points donnés et coéfficients d’ondelettes [Hölder exponents at given points and wavelet coefficients]
Language:
Format:
Source: ??? - C. R. Acad. Sci. Paris Série I, 308 (1989), 79–81. Translated by Robert D. Ryan.

Author: Jerome M. Shapiro
Title: Embedded image coding using zerotrees of wavelet coefficients
Language:
Format:
Source 1: Stanford University - IEEE Trans. Signal Processing, 41 (1993), 3445–3462.
Source 2: Tampereen teknillinen yliopisto

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Per Sjölin and Jan-Olov Strömberg
Spline systems as bases in Hardy spaces

papersincomputerscience.org
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1. Fundamental papers in wavelet theory