具有無邊界失真的多小波
A MULTIWAVELET WITH NON-BOUNDARY DISTORTION
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摘要: 多小波是近幾年小波理論研究的一個(gè)重要方向。該文綜述了多小波的重要性質(zhì),利用正交性和對(duì)稱性構(gòu)造了一個(gè)支集在[0,1]上具有精確重構(gòu)特性和二階逼近性的多小波,其最大特點(diǎn)是無邊界失真效應(yīng);經(jīng)平衡后,有更好的低通和高通特性,不用預(yù)濾波。實(shí)驗(yàn)結(jié)果表明重構(gòu)效果比單小波好。
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關(guān)鍵詞:
- 多小波; 精確重構(gòu); 邊界失真; 平衡小波
Abstract: The multiwavelet research has been an important aspect of the wavelet theory in recent years. This paper summarizes some important properties of multiwavelets. Using the properties of orthogonality and symmetry, A multiwavelet with compact support in [0,1], accurate reconstruction and approximation order 2 is constructed. The multiwavelet has the most advantage of non- boundary distortion. Needless to prefilter, it has better lowpass and highpass characteristics after being balanced. Examples of signal reconstruction and image compression are given, with satisfactory reconstruction results over the single wavelet. -
Jiang Qingtang, On the design of multifilter banks and orthonormal multiwavelet banks, IEEE Trans. on Signal Processing, 1998, SP-46(12), 3292-3302.[2]T.N.T. Goodman, S. L. Lee, Wavelets of multiplicity r, Trans. Amer. Math. Soc., 1994, 342(1), 307-324.[3]J.S. Geronimo, D. P. Hardin, P. R. Massopust, Fractal functions and wavelet expansions basedon several sealing functions, J. Approx. Theory, 1994, 78(3), 373-401.[4]I. Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conf., Ser. in Appl. Math., SIAM,Philadelphia, PA, 1992, 251-253. ［5］C.K. Chui, J-a. Lian, A study of orthonormal multi-wavelets, Appl. Numer. Math., 1996, 20(3),273-298.[5]X.G. Xia, A new prefilter design for discrete multiwavelet transforms, IEEE Trans. on SignalProcessing, 1998, SP-46(6), 1558-1570.[6]T.D. Bui, Chen G, Translation-invariant denoising using multiwavelets, IEEE Trans. on SignalProcesying, 1998, SP-46(12), 3414-3420.[7]J. Lebrun, M. Vetterli, Balanced multiwavelets theory and design, IEEE Trans. on Signal Pro-cessing, 1998, SP-46(4), 1119-1125. -
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