PDF(578 KB)
PDF(578 KB)
PDF(578 KB)
仿酉对称矩阵的构造及对称正交多小波滤波带的参数化
Construction of Paraunitary Symmetric Matrix and Parametrization of Symmetric and Orthogonal Multiwavelets Filter Banks
仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.), 给出o.s.m.的参数化. 恰当地选择一些参数,可得到具有一些优良性质的o.s.m., 例如Armlet.最后作这一个算例, 构造出一类对称的Chui--Lian Armlet滤波带.
Paraunitary matrices play a very important role in construction of wavelets, multiwavelets and frames. In this paper, we give an explicit algorithm for constructing paraunitary symmetric matrices (p.s.m. for short), whose components are symmetric or antisymmetric polynomials. Based on the constructed p.s.m. and the given orthogonal and symmetric multiwavelets (o.s.m. for short), parametrization of o.s.m. filter banks is given. Appropriately selecting some parameters, we can obtain o.s.m. with some additionally desirable properties such as Armlet. To embody our results, we construct a family of symmetric Chui--Lian Armlet filters.
多小波 / 正交 / 仿酉对称矩阵 {{custom_keyword}} /
paraunitary symmetric matrix / multiwavelets / orthogonal {{custom_keyword}} /
[1] Li Y. Z., A Class of Bidimensional FMRA Wavelet Frames , Acta Mathematica Sinica, English Series, 2006, 22(4): 1051--1062.
[2] Yang D. Y., Zhou X. W., Yuan Z. Z., Frame Wavelets with Compact Supports for L2(Rn) , Acta Mathematica Sinica, English Series, 2007, 23(2): 349--356.
[3] Selesnick I. W., Balanced multiwavelet bases based on symmetric fir filters, IEEE Transactions on Signal Processing, 2000, 48: 184--191.
[4] Petukhov A., Construction of symmetric orthogonal bases of wavelets and tight frames with integer dilation factor, Appl. Comput. Harmon. Anal, 2004, 17: 198--210.
[5] Jiang Q. T., Parameterizations of symmetric orthogonal multifilter banks with different filter lengths, Linear Algebra Appl., 2000, 311(1-3): 79--96.
[6] Shen L., Tan H. H., A characterization of symmetric/antisymmetric orthonormal length-4 multifilters, IEE Proceedings: Vision, Image and Signal Processing, 2001, 148(2): 103--106.
[7] Jiang Q. T., Symmetric paraunitary matrix extension and parameterizations of symmetric orthogonal multifilter banks, SIAM J. Matrix Anal Appl., 1996, 22: 723--737.
[8] Bhatt G., Johnson B. D. Weber E., Orthogonal wavelet frames and vector-valued wavelet transforms, Appl. Comput. Harmon. Anal., 2007, 23(2): 125--134.
[9] Yang S. Z., Peng L. Z., Construction of high order balanced multiscaling functions via PTST, Sci. China, Ser. F, 2006, 49(4): 504--515.
[10] Strela V., Multiwavelets: Theory and application, Deparment of Mathematics, Cambridge: Massachusetts Institute of Technology MA, 1996.
[11] Chui C. K., Lian J. A., Analysis-ready multiwavelets (armlets) for processing scalar-valued signals, IEEE, Signal Processing Letters, 2004, 11(2): 205--208.
[12] Chui C. K., Lian J. A., Armlets and balanced multiwavelets: flipping filter construction, IEEE Transactions on Signal Processing, 2005, 53: 1754--1767.
[13] Li Y. F., Yang S. Z., Zhu T. W., A family of balanced and analysis ready multiwavelets, Proceedings of 2007 International Conference on Wavelet Analysis and Pattern Recognition, 2007, 4: 1887--1890.
[14] Cui L. H., Wang W. X., Zhang J. M., On a family of biorthogonal armlets with prescribed properties, Appl. Math. Comput., 2007, 193(1): 36--65.
[15] Chui C. K., Lian Administrator A., Construction of orthonormal multi-wavelets with additional vanishing moments, Adv. Comput. Math., 2006, 24(1-4): 239--262.
广东省自然科学基金资助项目(05008289,032038);广东省博士科研启动基金资助项目(04300917)
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