Abstract
This chapter includes multiresolution decomposition for image analysis and data compression. Multiresolution processing has been implemented with many different architectures (tree structures) and filters (operators) for signal decomposition (analysis) and reconstruction (synthesis).1–13 Therefore, Section 5.1 begins with a single-level decomposition that most architectures share, and Section 5.2 extends the formulations to a particular multi-level realization, the wavelet transform. Finally, Section 5.3 characterizes the performance of this decomposition in the visual communication channel. This characterization focuses on the effects of the quantization of the wavelet transform coefficients (or requantization) on the information rate, data rate and image quality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Gabor, “Theory of communication,” Proc. IEEE 93, 429–457 (1946).
P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Comm. COM-31, 532–540 (1983).
I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. on Pure and Appl. Math., 41, 909–996 (1988).
S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoustic., Speech, and Signal Proc. ASSP-37, 2901–2110 (1989).
S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. on Pattern Recog. and Mach. Intell. 11, 674–693 (1989).
I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inform. Th. 36, 961–1005 (1990).
T. Ebrahimi and M. Kunt, “Image compression by Gabor expansion,” Opt. Eng. 30, 873–880 (1991).
J. W. Woods, editor, Subband Image Coding ( Kluwer Academic Publishers, Boston, 1991 ).
M. Vetterli and C. Herley, “Wavelets and filter banks: Theory and design,” IEEE Trans. Signal Proc. 40 (9), 2207–2232 (1992).
A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition ( Academic Press, Boston, 1992 ).
Y. Meyer, Wavelet: Algorithms and Applications ( SIAM, Philadelphia, 1993 ).
G. Kaiser, A Friendly Guide to Wavelets ( Birckhäuser, Boston, 1994 ).
M. Vetterli and J. Kovacevic, Wavelets and Subband Coding ( Prentice Hall, New Jersey, 1995 ).
S. Mallat and S. Zhong, “Wavelet maxima representation,” in Y. Meyer, editor, Wavelets and Applications ( Masson, Paris, 1991 ).
R. R. Coffman, Y. Meyer and M. V. Wickerhauser, “Wavelet analysis and signal processing,” in M. B. Ruskai et al., editor, Wavelets and their Applications ( Jones and Bartlett, Boston, 1992 ).
R. R. Coffman and M. V. Wickerhauser, “Entropy-based algorithms for best basis selection,” IEEE Trans. Inform. Th., Special Issue on Wavelet Transforms and Multiresolution Signal Analysis 38, 713–718 (1992).
J. M. Shapiro, “Embedded image coding using zero trees of wavelet coefficients,” IEEE Trans. Signal Proc., Special Issue on Wavelets and Signal Processing 41, 3445–3462 (1993).
K. Ramchandran and M. Vetterli, “Best wavelet packet bases in a rate-distortion sense,” IEEE Trans. Image Proc. 2 160–175 (1993).
D. Marr and E. Hildreth, “Theory of edge detection,” Proc. Roy. Soc. London B 207, 187–217 (1980).
D. Marr, Vision (Freeman, San Francisco, California, 1982 ).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Huck, F.O., Fales, C.L., Rahman, Zu. (1997). Multiresolution Decomposition. In: Visual Communication. The Springer International Series in Engineering and Computer Science, vol 409. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2568-1_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2568-1_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5180-9
Online ISBN: 978-1-4757-2568-1
eBook Packages: Springer Book Archive