SPECTRAL RADIUS OF BIORTHOGONAL WAVELETS WITH ITS APPLICATION Zou, Qingyun; Wang, Guoqiu; Yang, Mengyun;
In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.
2-circular matrix;biorthogonality;vanishing moments;filters of even lengths;image compression;
A. Cohen, I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Commu. Pure Appl. Math. 45 (1992), no. 5, 485-560.
I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), no. 7, 909-996.
I. Daubechies, Ten Lectures on Wavelets, Philadelphia, SIAM Pub., 1992.
H. O. Kim, R. Y. Kim, Y. J. Lee, and J. Yoon, Quasi-interpolatory refinable functions and construction of biorthogonal wavelet systems, Adv. Comput. Math. 33 (2010), no. 3, 255-283.
T. L. Li, Characters of circular matrix, Science Bulletin in Chinese 2 (1982), 30-33.
T. Q. Nguyen and P. P. Vaidyanathan, Two-channel perfect reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters, IEEE Trans. Acoustics Speech Signal Process. 37 (1989), 676-690.
A. Said and W. A. Pearlman, A new, fast and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits System Video Tech. 6 (1996), 243-250.
W. Sweldens, The lifting scheme: a constructing of second generation wavelet, SIAM. Math. Anal. 29 (1998), no. 2, 511-546.
M. Vetterli and D. L. Gall, Perfect reconstruction FIR filter banks, some properties and factorizations, IEEE Trans. Acoust. Speech, Signal Process. 37 (1989), no. 7, 1057-1071.
G. Q. Wang, Matrix methods of constructing wavelet filters and discrete hyper-wavelet transforms, Opt. Eng. 39 (2000), no. 4, 1080-1087.
G. Q. Wang and W. W. Yuan, Generic 9-7 tap wavelets filters and their performance studies on image compression, Acta. Electron. Sin. 29 (2001), 130-132.
G. Q. Wang and W. W. Yuan, Optimal model for biorthogonal wavelet filters, Opt. Eng. 42 (2003), no. 2, 350-356.