Abstract
The concept of a transform is familiar to mathematicians. It is a standard mathematical tool used to solve problems in many areas. The idea is to change a mathematical quantity (a number, a vector, a function, or anything else) to another form, where it may look unfamiliar but may exhibit useful features. The transformed quantity is used to solve a problem or to perform a calculation, and the result is then transformed back to the original form.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Lewalle, Jacques (1995) “Tutorial on Continuous Wavelet Analysis of Experimental Data,” available anonymously from ftp.mame.syr.edu/pub/jlewalle/tutor.ps.Z.
Rao, Raghuveer M., and Ajit S. Bopardikar (1998) Waveiet Transforms: Introduction To Theory and Applications, Reading, MA, Addison-Wesley.
Mulcahy, Colm (1996) “Plotting and Scheming with Wavelets,” Mathematics Magazine, 69(5):323–343, December. Also available as http://www.spelman.edu/-colm/csam.ps.
Mulcahy, Colm (1997) “Image Compression Using the Haar Wavelet Transform,” Spel-man College Science and Mathematics Journal, 1(1):22–31, April. Also available as http://www.spelman.edu/-colm/wav.ps. (It has been claimed that any smart 15 year old could follow this introduction to wavelets.)
Stollnitz, E. J., T. D. DeRose, and D. H. Salesin (1996) Wavelets for Computer Graphics, San Francisco, CA, Morgan Kaufmann.
Simoncelli, Eero P. and Edward. H. Adelson (1990) “Subband Transforms,” in John Woods, editor, Subband Coding, Boston, Kluwer Academic Press, 143–192.
Strang, Gilbert and Truong Nguyen (1996) Wavelets and Filter Banks, Wellesley, MA, Wellesley-Cambridge Press.
Akansu, Ali, and R. Haddad (1992) Multiresolution Signal Decomposition, San Diego, CA, Academic Press.
Daubechies, Ingrid (1988) “Orthonormal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, 41:909–996.
Burt, Peter J., and Edward H. Adelson (1983) “The Laplacian Pyramid as a Compact Image Code,” IEEE Transactions on Communications, COM 31(4):532–540, April.
Mallat, Stephane (1989) “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Trans, on Pattern Analysis and Machine Intelligence, 11(7):674–693, July.
Meyer, F. G., A. Averbuch, and J.O. Strömberg (1998) “Fast Adaptive Wavelet Packet Image Compression,” submitted to the IEEE Transactions on Image Processing, revised June 1999.
Starck, J. L., F. Murtagh, and A. Bijaoui (1998) Image Processing and Data Analysis: The Multiscale Approach, Cambridge University Press.
Strømme, øyvind and Douglas R. McGregor (1997) “Comparison of Fidelity of Reproduction of Images After Lossy Compression Using Standard and NonStandard Wavelet Decompositions,” in Proceedings of The First European Conference on Signal Analysis and Prediction (ECSAP 97), Prague, June. Also downloadable from http://homepages.strath.ac.uk/-cadu02/research/publications.html.
Strømme, øyvind (1999) On The Applicability of Wavelet Transforms to Image and Video Compression, Ph.D. thesis, University of Strathclyde, February.
Wong, Kwo-Jyr, and C. C. Jay Kuo (1993) “A Full Wavelet Transform (FWT) Approach to Image Compression,” Image and Video Processing, Bellingham, WA, SPIE volume 1903:153–164.
Stollnitz, E. J., T. D. DeRose, and D. H. Salesin (1996) Wavelets for Computer Graphics, San Francisco, CA, Morgan Kaufmann.
Sweldens, Wim and Peter Schröder (1996), Building Your Own Wavelets At Home, SIG-GRAPH 96 Course Notes, available on the WWW.
Burt, Peter J., and Edward H. Adelson (1983) “The Laplacian Pyramid as a Compact Image Code,” IEEE Transactions on Communications, COM 31(4):532–540, April.
Said, A., and W. A. Pearlman (1996), “A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees,” IEEE Transactions on Circuits and Systems for Video Technology, 6(6):243–250, June.
Banister, Brian and Thomas R. Fischer (1999) “Quadtree Classification and TCQ Image Coding,” in Storer, James A., and Martin Cohn (eds.) (1999) DCC’ 99: Data Compression Conference, Los Alamitos, CA, IEEE Computer Society Press, pp. 149–157.
Joshi, R. L., V. J. Crump, and T. R. Fischer (1993) “Image Subband Coding Using Arithmetic and Trellis Coded Quantization,” IEEE Transactions on Circuits and Systems Video Technology, 5(6):515–523, December.
Adelson, E. H., E. Simoncelli, and R. Hingorani (1987) “Orthogonal Pyramid Transforms for Image Coding,” Proceedings SPIE, vol. 845, Cambridge, MA, pp. 50–58, October.
Shapiro, Jerome M. (1993) “Embedded Image Coding Using Zerotrees of Wavelet Coefficients,” IEEE Transactions on Signal Processing, 41(12):3445–3462, October.
ATT (1996) is URL http://www.djvu.att.com/.
Haffner, Patrick et al. (1998) “High-Quality Document Image Compression with DjVu,” Journal of Electronic Imaging, 7(3):410–425, SPIE. This is also available from URL http://www.research.att.com/-leonb/biblio. html.
Bradley, Jonathan N., Christopher M. Brislawn, and Tom Hopper (1993) “The FBI Wavelet/Scalar Quantization Standard for Grayscale Fingerprint Image Compression,” Proc. of Visual Information Processing II, Orlando, FL, SPIE v. 1961, pp. 293–304, April.
Brislawn, Christopher, Jonathan Bradley, R. Onyshczak, and Tom Hopper (1996) “The FBI Compression Standard for Digitized Fingerprint Images,” in Proceedings SPIE, v. 2847, Denver, CO, pp. 344–355, August.
Federal Bureau of Investigations (1993) WSQ Grayscale Fingerprint Image Compression Specification, ver. 2.0, Document #IAFIS-IC-0110v2, Criminal Justice Information Services, February.
ISO/IEC (2000), International Standard IS 15444-1 “Information Technology—JPEG 2000 Image Coding System.” This is the FDC (final committee draft) version 1.0, 16 March 2000.
JPEG 2000 Organization (2000) is at URL http://www.jpeg-org/JPEG2000.htm.
Taubman, David (1999) “High Performance Scalable Image Compression with EBCOT,” to appear in IEEE Transactions on Image Processing. This is currently available from = http://maestro.ee.unsw.edu.au/-taubman/activities/preprints/ebcot.pdf.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Salomon, D. (2000). Wavelet Methods. In: Data Compression. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86092-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-86092-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78086-1
Online ISBN: 978-3-642-86092-8
eBook Packages: Springer Book Archive