Abstract
We present a study on applications of multiwavelet analysis to image compression, where filter coefficents form matrices. As a multiwavelet filter bank has multiple channels of inputs, we investigate the data initialization problem by considering prefilters and postfilters that may give more efficient representations of the decomposed data. The interpolation postfilter andp refilter are formulated, which are capable to provide a better approximate image at each coarser resolution level. A design process is given to obtain both filters having compact supports, if exist. Image compression performances of some multiwavelet systems are studied in comparison to those of single wavelet systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chui, C. K.: An Introduction to Wavelets. Volume 1 of Wavelet Analysis and Its Applications. Academic Press (1992)
Geronimo, J. S., Hardin, D. P., Massopust, P. R.: Fractal functions and wavelet expansions basedo on several scaling functions. Journal of Approximation Theory 78 (1994) 373–401
Donovan, G. C., Geronimo, J., Hardin, D. P.: Intertwining multiresolution analyses and the construction of piecewise polynomial wavelets. SIAM Journal of Mathematical Analysis 27 (1996) 1791–1815
Donovan, G., Geronimo, J. S., Hardin, D. P., Massopust, P. R.: Construction of orthogonal wavelets using fractal interpolation functions. SIAM Journal of Mathematical Analysis 27 (1996) 1158–1192
Strela, V., Walden, A. T.: Orthogonal and biorthogonal multiwavelets for signal denoising and image compression. SPIE Proc. 3391 AeroSense 98, Orlando, Florida, April 1998 (1998)
Selesnick, I.W.: Interpolating multiwavelet bases andt he sampling theorem. IEEE Trans. on Signal Processing 47 (1999) 1615–1621
Chui, C. K., Lian, J.: A study on orthonormal multi-wavelets. J. Appl. Numer. Math. 20 (1996) 273–298
Vaidyanathan, P. P.: Multirate Systems and Filter Banks. Prentice-Hall, New Jersey (1993)
Strela, V.: Multiwavelets: Theory andA pplications. PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass. (1996)
Plonka, G., Strela, V.: Construction of multiscaling functions with approximation ands ymmetry. SIAM Journal of Mathematical Analysis 29 (1998) 481–510
Xia, X. G., Geronimo, J. S., Hardin, D. P., Suter, B. W.: Design of prefilters for discrete multiwavelet transforms. IEEE Trans. on Signal Processing 44 (1996) 25–35
Xia, X. G.: A new prefilter design for discrete multiwavelet transforms. IEEE Trans. on Signal Processing 46 (1998) 1558–1570
Miller, J. T., Li, C. C.: Adaptive multiwavelet initialization. IEEE Trans. on Signal Processing 46 (1998) 3282–3291
Xia, T., Jiang, Q.: Optimal multifilter banks: design, related symmetric extension transform andap plication to image compression. IEEE Trans. on Signal Processing 47 (1999) 1878–1889
Jiang, Q.: On the design of multifilter banks and orthogonal multiwavelet bases. IEEE Trans. on Signal Processing 46 (1998) 3292–3303
Strela, V., Heller, P., Strang, G., Topiwala, P., Heil, C.: The application of multiwavelet filter banks to image processing. IEEE Trans. on Image Processing 8 (1999) 548–563
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kim, W., Li, CC. (2001). A Study on Preconditioning Multiwavelet Systems for Image Compression. In: Tang, Y.Y., Yuen, P.C., Li, Ch., Wickerhauser, V. (eds) Wavelet Analysis and Its Applications. WAA 2001. Lecture Notes in Computer Science, vol 2251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45333-4_6
Download citation
DOI: https://doi.org/10.1007/3-540-45333-4_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43034-6
Online ISBN: 978-3-540-45333-8
eBook Packages: Springer Book Archive