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Multiwavelet prefilters--part II: optimal orthogonal prefilters
K Attakitmongcol1, D P Hardin, D M Wilkes
1Sch. of Electr. Eng., Suranaree Univ. of Technol., Thailand. kitti@ccs.sut.ac.th
Summary
This study introduces two novel methods for optimizing prefilters in unbalanced multiwavelet applications. Optimal prefilters were developed for DGHM and Chui-Lian (CL) multiwavelets, enhancing signal processing and image compression.
Area of Science:
- Signal Processing
- Applied Mathematics
- Image Analysis
Background:
- Prefiltering is crucial for discrete signals in unbalanced multiwavelet applications.
- Orthogonal multiwavelet bases require effective prefiltering for optimal performance.
Purpose of the Study:
- To develop and present two distinct methods for obtaining optimal second-order approximation preserving prefilters.
- To apply these methods to DGHM and Chui-Lian (CL) multiwavelets.
- To evaluate the performance of these optimized prefilters in image compression.
Main Methods:
- Developing two prefilter optimization schemes based on prefilter construction from part I.
- Utilizing Taylor series expansion of the prefilter and multiwavelet for the first scheme.
- Minimizing the energy compaction ratio (ECR) of wavelet coefficients for the second scheme.
Main Results:
- Optimal second-order approximation preserving prefilters were derived for DGHM and CL multiwavelets.
- Experimental comparison in an image compression scheme demonstrated the effectiveness of the optimized prefilters.
- Quadratic input signals were found to be annihilated by the high-pass filter bank with DGHM multiwavelets and optimized prefilters.
Conclusions:
- The developed methods provide effective means to obtain optimal prefilters for unbalanced multiwavelet systems.
- Optimized prefilters significantly improve performance in applications like image compression.
- The study highlights specific signal annihilation properties with certain multiwavelet-prefilter combinations.
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