DocumentCode :
1533767
Title :
Multiwavelet prefilters. II. Optimal orthogonal prefilters
Author :
Attakitmongcol, Kitti ; Hardin, Douglas P. ; Wilkes, D. Mitchell
Author_Institution :
Sch. of Electr. Eng., Suranaree Univ. of Technol., Thailand
Volume :
10
Issue :
10
fYear :
2001
fDate :
10/1/2001 12:00:00 AM
Firstpage :
1476
Lastpage :
1487
Abstract :
For pt.I see IEEE Trans. Circuits Syst. II, vol.45, p.1106-12 (1998). Prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets. In this paper, we develop two methods to obtain optimal second-order approximation preserving prefilters for a given orthogonal multiwavelet basis. These procedures use the prefilter construction introduced in Hardin and Roach (1998). The first prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. The second one is achieved by minimizing the energy compaction ratio (ECR) of the wavelet coefficients for an experimentally determined average input spectrum. We use both methods to find prefilters for the cases of the DGHM and Chui-Lian (CL) multiwavelets. We then compare experimental results using these filters in an image compression scheme. Additionally, using the DGHM multiwavelet with the optimal prefilters from the first scheme, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition
Keywords :
approximation theory; channel bank filters; circuit optimisation; data compression; image coding; wavelet transforms; Chui-Lian multiwavelets; DGHM multiwavelets; Taylor series expansion; average input spectrum; discrete signal; energy compaction ratio; filter bank; high-pass portion; image compression scheme; multiwavelet prefilters; optimal orthogonal prefilters; optimal second-order approximation preserving prefilters; orthogonal multiwavelet basis; prefilter optimization scheme; quadratic input signals; unbalanced multiwavelets; wavelet coefficients; Compaction; Filter bank; Image coding; Mathematics; Polynomials; Taylor series; Wavelet coefficients;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.951534
Filename :
951534
Link To Document :
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