PDF(411 KB)
PDF(411 KB)
PDF(411 KB)
高维Riesz多小波基
Multivariate Riesz Multiwavelet Bases
本文研究了(L2(Rs))r×1上的短支集高维Riesz多小波基, 它在很多领域比如图像处理,计算机图形学,数值算法都有重要的应用.刻画了从向量细分函数得到Riesz基的算法,也给出了Riesz小波基在(L2(Rs))r×1空间上的一些重要的结论.
In this paper, we will investigateMultivariate Riesz Multiwavelet Bases with short support in (L2(Rs))r×1, which have applications in many areas, such as image processing, computer graphics and numerical algorithms. We characterize an algorithm to derive Riesz bases from refinable function vectors. Several other important results about Riesz wavelet bases in (L2(Rs))r×1 are also given.
Riesz小波基 / 细分方程 / Bessel {{custom_keyword}} /
Riesz wavelet bases / refinement equation / Bessel {{custom_keyword}} /
[1] Jia R. Q., Micchelli C. A., Using the Refinement Equation for the Construction of Pre-wavelet II: Power of two, Curves and Surfaces, New York: Academic Press, 1991: 209--246.
[2] Cohen A., Daubechies I., A New Technique to estimate the regularity of refinable functions, Rev. Mat. Iberoamericana, 1996, 12: 527--591.
[3] Han B., On a conjecture about MRA Riesz wavelet basis, Proc. Amer. Math. Soc., 2006, 134: 1973--1983.
[4] Han B., Jia R. Q., Multivariate refinement equations of convergence of subdivision schemes, SIAM J. Math. Anal., 1998, 29: 1177--1199.
[5] Han B., Jia R. Q., Characterization of Riesz bases of wavelets generated from multiresolution analysis, Appl. Comput. Harmon. Anal., 2007, 23: 321--345.
[6] Han B., Shen Z. W., Wavelets from the Loop scheme, J. Fourier Anal. Appl., 2005, 11: 615--637.
[7] Han B., Shen Z. W., Wavelets with short support, SIAM J. Math. Anal., 2006, 38: 530--556.
[8] Han B., Kwon S., Park S. S., Riesz multiwavelet bases, Appl. Comput. Harmon. Anal., 2006, 20: 161--183.
[9] Jia R. Q., Wang J. Z., Zhou D. X., Compactly supported wavelet bases for Sobolev spaces, Appl. Comput. Harmon. Anal., 2003, 15: 224--241.
[10] Li S., Xian J., Biorthogonal multiple wavelets generated by vector refinement equation, Sci., China, Ser. A Math., 2007, 50: 1015--1025.
[11] Li S., Liu Z. S., Riesz multiwavelet bases generated by vector refinement equation, Sci, China, Ser. A Math., 2009, 52: 468--480.
[12] Dahmen W., Wavelet and multiscale methods for opertor equations, Acta Number, 1997, 6: 55--228.
[13] Han B., Vector cascade algorithms and refinable function vectors in Sobolev spaces, J. Approx. Theory, 2003, 124: 44--88.
[14] Jia R. Q., Characterization of smothness of multivariate refinable function in Sobolev spaces, Trans. Amer. Math. Soc., 1999, 351: 4089--4112.
[15] Jia R. Q., Jiang Q. T., Approximation power of refinable vectors of functions, in wavelet analysis and applications (Guangzhou, 1999), 155-178, AMS/IP Stud. Adv. Math., 25, Amer. Math. Soc., Providence, RI, 2002.
[16] Ron A., Shen Z. W., The Sobolev regularity of refinable functions, J. Approx. Theory, 2000, 106: 185--225.
[17] Shen Z. W., Refinable function vectors, SIAM J. Math. Anal., 1998, 29: 235--250.
[18] Daubechies I., Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics, SIAM, Philadelphia, 1992.
[19] Han B., Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dialation matrix, J. Comput. Appl. Math., 2003, 155: 43--67.
[20] Han B., On dual wavelet tight frames, Appl. Comput. Harmon. Anal., 1997, 4: 380--413.
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