Wavelet Beginners Bibliography, Some with Code

We all have to start somewhere.. The following references are selected for ease of understanding by someone unfamiliar with the signal processing literature. The easiest are listed first. (Thanks to Gerard Middleton for the initial list!)

(1)
Barry A. Cipra, "Wavelet Applications Come to the Fore," SIAM News (Mathematics that Counts), 11/93.
Red Button Wavelet Applications article.
(2)
Barbara Burke Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, A.K. Peters, 1995.
Red Button The World According to Wavelets.
(3)
G. Strang, "Wavelets," American Scientist, Vol. 82, 1994, pp. 250-255.
(4)
Edward Aboufadel and Steven Schlicker, Discovering Wavelets, Wiley-Interscience, November 1999.
You can download software to use with the book from the authors' website.
Red Button Discovering Wavelets - the book
Red Button Discovering Wavelets - software
(5)
Rioul, Olivier and Martin Vetterli, "Wavelets and signal processing," IEEE Signal Processing Magazine, October 1991, p.14-38.
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G. Strang, "Wavelet transforms versus Fourier transforms," Bull. (New Series) Amer. Math. Soc., Vol. 28, No. 2, 1993, pp. 288-305.
(7)
Colm Mulcahy, "Plotting & Scheming with Wavelets." An elementary, linear algebra-based intro to wavelets aimed at a mathematical audience with little sophistication. It was awarded a 1996 Carl B. Allendoerfer Award by the Mathematical Association of America (MAA ) at MathFest '97 in Atlanta, August 1997. This paper is published in Mathematics Magazine, Vol 69, No 5, December 1996, 323-343, a publication of the Mathematical Association of America. A postscript form of the article with associated Matlab m-files can be found at the sites below.
Red Button Mulcahy's Papers and some information on a wavelet mini-course.
Red Button "Plotting & Scheming with Wavelets" (ps, 1325K).
(8)
Robinson, Sam L. and Ryczek, Peter F., "Wavelets," The Mathematica Journal, Volume 5, Issue 1, Winter 1995, pp. 74-81.
The code can be purchased separately on a MS-DOS or Macintosh diskette.
Red Button The Mathematica Journal, Volume 5, Issue 1.
(9)
Rowe, Alistair C.H. and Abbott, Paul C., "Daubechies Wavelets and Mathematica," Computers in Physics, Volume 9, Issue 6, November/December 1995, pp. 635-648.
This article is very similar in content to the above The Mathematica Journal article. (Both are very nice articles.) The paper can be downloaded in Microsoft Word, self-extracting, Macbinary format. The code can be downloaded to supplement the article: WaveletTransform.m You can also retrieve from the below site Abbott's Wavelets course Wavelets.nb and Abbott's version of Daubechies and Swelden's Lifting Scheme Lifting.nb as Mathematica 3.0 Notebooks.
Red Button Computers in Physics, November/December 1995 wavelets article
Red Button Abbott's supplementary wavelets code.
(10)
Paul S Addison, The Illustrated Wavelet Transform Handbook. I have used this book; the 'illustrated' approach works well. From the book jacket: This book provides an overview of the theory and practical application of wavelet transform methods. It is designed specifically for the 'applied' reader in science, engineering, medicine, finance or any other of the growing number of application areas. Newcomers to the subject will find an accessible and clear account of the theory of continuous and discrete wavelet transforms with a large number of examples of their use across a wide range of disciplines.
Red Button The Illustrated Wavelet Transform Handbook.
(11)
"Wavelets for Kids" by B. Vidakovic.
Red Button Part One, and Red Button Part Two.
(12)
Phillies, George D.J., "Wavelets: A New Alternative to Fourier Transforms", Computers in Physics, Volume 10, Issue 3, May/June 1996, pp. 247-252.
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Hoffman, Meredith, "Wavelet Analysis: Revolutionary tool for Data Analysis and Signal Processing", SciTech Journal, Volume 6, Number 9, September/October 1996, pp. 19-22.
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Bruce, Andrew, Donoho, David, and Gao, Hong-Ye, "Wavelet Analysis", IEEE Spectrum, October 1996, pp. 26-35.A good broad non-technical overview of wavelet analysis with an emphasis on wavelet software.
(15)
Nievergelt, Yves, Wavelets Made Easy, 2nd printing, 2001, 310 p. 53 illus., Hardcover.
I haven't browsed this book with my own eyes yet. The description from the Wavelet Digest a few years ago says: "Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines -- computer science, engineering, mathematics, mathematical sciences -- as well as for practicing professionals in these areas."
Red Button Wavelets Made Easy.
(16)
E.J. Stollnitz and T.D. DeRose and D.H. Salesin, "Wavelets for Computer Graphics: Theory and Application, Morgan Kaufmann Publishers, 1996. This material came from the works: "Wavelets for Computer Graphics: A Primer, Parts 1 and 2," IEEE Computer Graphics and Applications, May 1995 (Part 1), July 1995 (Part 2). The link goes to the book at amazon. I like this book, their approach of focusing on the Haar wavelet works well.
Red Button Wavelets for Computer Graphics.
(17)
Press, William; Teukolsky, Saul; Vetterling, William; Flannery, Brian 1992. Numerical Recipes in Fortran (or C), NY, NY: Cambridge University Press.
The wavelet routines can be freely copied and redistributed. (UNLIKE much of the rest of the Numerical Recipes code.)
Red Button Numerical Recipes Wavelets Software.
(18)
Jaideva C. Goswami and Andrew K. Chan Fundamentals of Wavelets: Theory, Algorithms, and Applications, Wiley, 1999. From a comp.dsp person who says that this book is readable, and a good introduction to wavelets.
Red Button Fundamentals of Wavelets.
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Ola Bratteli and Palle E. T. Jorgensen Wavelets through a Looking Glass: The World of the Spectrum, Birkhaeuser, 2002.
Red Button Wavelets through a looking glass.
(20)
S. G. Mallat, "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol II, 7, 1989, pp. 674-693.
(21)
Meyer, Yves, "Review of two books on wavelets," Bull. (New Series) Amer. Math. Soc., Vol. 28, No. 2, 1993, pp. 350-360.
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I. Daubechies, "Where do wavelets come from? (A personal point of view)," Proceedings of the IEEE, Special Issue on Wavelets, 84 (no. 4), pp. 510--513, April 1996.
(23)
Y. Meyer, and R. Ryan Wavelets: Algorithms and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 1993. This was my very first wavelet book. Easy to read and compact...
Red Button Book and Red Button Review.
(24)
Y T Chan, Wavelet Basics, Kluwer Academic Publishers,1995. The link goes to amazon.
Red Button Wavelet Basics
(25)
Christian Blatter, Wavelets: A Primer, AK Peters, 1999.
Red Button Wavelets: A Primer
(26)
Crandall, Richard, Projects in Scientific Computation, NY, NY: Springer- Verlag, 1994, pp. 197-226.
This book has C and Mathematica code.
Red Button Projects in Scientific Computation
(27)
Randy K. Young, Wavelet Theory and its Applications, Kluwer Academic Publishers, 1993.
Red Button Wavelet Theory and its Applications
(28)
M. Vetterli and C. Herley, "Wavelets and Filter Banks: Theory and Design," IEEE Transactions on Signal Processing, Vol. 40, 1992, pp. 2207-2232.
(29)
Donald B. Percival and Andrew T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000. (Many useful things at the web site from filters to time series.)
Red Button Wavelet Methods for Time Series Analysis.
(30)
Cohen, Jack and Chen, Tong 1993; "Fundamentals of the Discrete Wavelet Transform for Seismic Data Processing," unpublished. An excellent tutorial about the wavelet transform, including 2D wavelets. See also their other equally excellent wavelet papers at their site. To Dr. Cohen. In Memorandum
Red Button Cohen and Chen DWT Fundaments.
Red Button Other Wavelet Articles and Mathematica Software.
(31)
Navarro, Rafael; Tabernero, Antonio; and Cristobal, Gabriel, 1995; "Image Representation with Gabor Wavelets and its Applications," to be published in Advances in Imaging and Electron Physics. An excellent applications-oriented paper (light on the math, and heavy on the illustrations) about the Gabor wavelet. Topics include: joint space-frequency representations and wavelets, Gabor schemes of representation, vision modeling, image coding, enhancement and reconstruction, analysis and machine vision.
Red Button Representation with Gabor Wavelets Paper.
Red Button Figures for Representation with Gabor Wavelets Paper.
(32)
Wim Sweldens and Peter Schroeder; "Building your own wavelets at home". Readable, practical paper.
Red Button Building Your Own Wavelets At Home.
(33)
A Wavelet Tour of Signal Processing by Stephane G. Mallat. Academic Press; 2nd edition (September 15, 1999). I presently use this book more than any other for learning more in-depth wavelet ideas and algorithms. It's best to complement this book with wavelet software such as Stanford's WaveLab Matlab Software.
Red Button A Wavelet Tour of Signal Processing
(34)
Gilbert Strang and Truong Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996. This is perhaps the first real wavelet textbook. Very readable and designed to teach those needing to get their hands in the algorithms. (Yes, it's technical.) The Table of Contents and Guide to the Book can be seen in their homepage.
Red Button Wavelets and Filter Banks.
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JL Starck, F Murtagh, A Bijaoui, Image and Data Analysis: The Multiscale Approach, Cambridge University Press, 1998. I have not used this yet, but some of my astronomy colleagues have used it and like it.
Red Button Image and Data Analysis
(36)
Arne Jensen and Anders la Cour-Harbo, Ripples in Mathematics: The Discrete Wavelet Transform, Springer Verlag 2001.
Red Button Ripples in Mathematics.
(37)
O.M. Nielsen, Wavelets in Scientific Computing, Ph.D. dissertation. (12.5Mb, 246 pages), 1998.
Red Button Wavelets in Scientific Computing.
(38)
Edited by J. C. van den Berg, Many authors; Wavelets in Physics, Cambridge University Press, 2004 (paper). This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. [This book is in my reading queue.]
Red Button Wavelets in Physics.
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Various Wavelet Researchers; "Wavelets and Their Applications in Computer Graphics," Wavelets course organized by Alain Fournier for SIGRAPHs '94 and '95. They are in the form of a (UNIX) compressed file 3.4MB in size that uncompresses to an 11.0MB PostScript file. The printed document is 239 pages long. These notes are provided through the courtesy of Dr. Fournier.
Red Button SIGRAPH Computer Graphics Wavelet Course.
(40)
Cody, Mac A., "The Fast Wavelet Transform," Dr. Dobb's Journal, April 1992.
Red Button Fast Wavelet Transform Article by Mac Cody.
(41)
Cody, Mac A., "A Wavelet Analyzer," Dr. Dobb's Journal, April 1993.
Red Button A Wavelet Analyzer Article by Mac Cody.
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Cody, Mac A., "The Wavelet Packet Transform," Dr. Dobb's Journal, April 1994.
Red Button The Wavelet Packet Transform Article by Mac Cody.
(43)
Daubechies, Ingrid, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics Press, vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia, 1992. This is the classic wavelet book.
Red Button Ten Lectures on Wavelets
(44)
Wickerhauser Victor, Adapted Wavelet Analysis from Theory to Software, AK Peters, Boston, 1994.
This book was my second wavelet book, and about the most practical wavelet book I own. This book has C code.
Red Button Adapted Wavelet Analysis book and Red Button List of Errata in PS, dvi, and TeX format.
(45)
David F. Walnut, An Introduction to Wavelet Analysis, Birkhauser, Boston, 2002.
B. Treadway has given enthusiastically high marks for this book, his review can be seen below.
Red Button Review (PDF) and book.
(46)
Mark Pinsky, Introduction to Fourier Analysis and Wavelets, Brooks-Cole, 2001. This book is unique in combining a mathematically rigorous treatment of classical Fourier Analysis with a definitve final chapter on one-dimensional wavelets. For the upper undergraduate or beginning graduate level.
Red Button Introduction to Fourier Analysis and Wavelets
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Daubechies, Ingrid, "Orthonormal Bases of Compactly Supported Wavelets," Comm. Pure Appl. Math., Vol 41, 1988, pp. 906-966.
(48)
Newland, D.E., An Introduction to Random Vibrations, Spectral and Wavelet Analysis, New York, John Wiley, 1993. I really like this book: Extremely clear and easy to read, interesting examples. Because of its high cost, I drooled over it for a long while before buying. Since then, I never regretted spending the money. The third edition of the book has a few Matlab scripts. A somewhat more extensive collection is available from him at: Lynxvale Limited, 20 Trumpington Street, Cambridge CB2 1QA U.K.
Red Button An Introduction to Random Vibrations, Spectral and Wavelet Analysis.
(49)
Martin Vetterli and Jelena Kovacevic, Wavelets and Subband Coding, Prentice-Hall, New Jersey, 1995.
Red Button Wavelets and Subband Coding
(50)
Ali N. Akansu and Richard A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, Wavelets, Academic Press, Inc., ISBN 0-12-047140-X.
Red Button Multiresolution Signal Decomposition
(51)
T. Masters, Signal and Image Processing with Neural Networks, Wiley. A good reference for the applications of the Gabor Transform in image processing. It includes disk with source code.
Red Button Signal and Image Processing with Neural Networks.
(52)
Weiss, L. G., "Wavelets and Wideband Correlation Processing," IEEE Transactions on Signal Processing, January 1994, p13-32.
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Argoul, F. et al., "Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade," Nature, Vol. 338, 1989, pp. 51-53.
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Farge, Marie, "Wavelet transforms and their application to turbulence," Ann. Rev. Fluid Mech. Vol. 24, 1989, pp.395-457.
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Muzy, J.F., E. Bacry and A. Arneodo, "The multifractal formalism revisited with wavelets," Internatl. Jour. Bifurcation Chaos, Vol. 4, No. 2, 1994, pp.245-302.
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D. Donoho, "Nonlinear Wavelet Methods for Recovery of Signals, Densities, and Spectra from Indirect and Noisy Data," Different Perspectives on Wavelets, Proceeding of Symposia in Applied Mathematics, Vol 47, I. Daubechies ed. Amer. Math. Soc., Providence, R.I., 1993, pp. 173-205.
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Wickerhauser, M.V., "Acoustic Signal Compression with Wave Packets," 1989.
Red Button Index of Papers and TeX Paper.
(58)
Kaiser,G., A Friendly Guide to Wavelets, Birkhauser, Boston, 1994.
Red Button A Friendly Guide to Wavelets and related courses.
(59)
John R. Smith and Shih-Fu Chang, "Frequency and Spatially Adaptive Wavelet Packets," Proceedings of the I.E.E.E. International Conference on Acoustics, Speech and Signal Processing (ICASSP-95), Birkhauser, Boston, 1994.
Red Button Frequency and Spatially Adaptive Wavelet Packets.
(60)
Jean-Luc Starck and Fionn Murtagh and Albert Bijaoui, "Image Restoration with Denoising Using Multi-Resolution," (unpublished?).
Red Button Image Restoration with Denoising.
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Scargle, J. et al., "The Quasi-Periodic Oscillations and Very Low Frequency Noise of Scorpius X-1 as Transient Chaos: A Dripping Handrail?,"The Astrophysical Journal, Vol. 411, 1993, L91-L94.
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J. Bradley, C. Brislawn, and T. Hopper, "The FBI Wavelet/Scalar Quantization Standard for Gray-scale Fingerprint Image Compression" Tech. Report LA-UR-93-1659 Los Alamos Nat'l Lab, Los Alamos, N.M. 1993. See also C. Brislawn's WWW FBI site.
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Peter Schroder and Pat Hanrahan, "Wavelet Methods for Radiance Computations." Eurographics Workshop on Rendering, June 1994.
Red Button Wavelet Methods for Radiance Computations.
(64)
Peter Schroeder, Wim Sweldens, David Salesin, Tony DeRose, Michael Cohen, 1996 SIGGRAPH: Wavelets in Computer Graphics Course.
Red Button SIGGRAPH Computer Graphics Course.
(65)
S. Jaffard, Y. Meyer, and R. Ryan Wavelets: Tools for Science and Technology, Society for Industrial and Applied Mathematics, Philadelphia, 2001. This book began as a one-chapter revision of the book by Y. Meyer (Wavelets: Algorithms and Applications). It is for people who don't mind the math, but it is still relatively readible.
Red Button Wavelets: Tools for Science and Technology.
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R. Carmona, W. Hwang, B. Torresani, Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S Academic Press, 1998. For those who don't mind the math. For me, the useful aspect is the code snippets in S.
Red Button Practical Time-Frequency Analysis.
(67)
(Many Participants) Wavelet And Multifractal Analysis 2004 Summer School.
Red Button Some of the Lectures.



For more global access: Links to (all) wavelet books at amazon:
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Links to wavelet books at Amazon.com.
Red Button Wavelet Books at amazon.com
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Links to wavelet books at Amazon.co.uk.
Red Button Wavelet Books at amazon.co.uk
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Links to wavelet books at Amazon.de.
Red Button Wavelet Books at amazon.de

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Last Modified by Amara Graps on 15 July 2006.
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