通用双正交小波构造方法的研究
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摘要
小波在信号分析、图象处理、模式识别、计算机视觉等方面得到了越来越广泛的应用，而此（小波）领域中的双正交小波的研究正在进行之中，尽管有些作者已收集了几种这样的滤波器和相关的双正交小波，但应用效果不佳，而且应用领域狭窄，由本文提供的双正交小波构造方法，实验证明，效果良好，且具有较强的通用性，除可用在信号分析、图象处理、模式识别、计算机视觉领域外，还在数学、通信、地震、化学等领域有广泛的应用前景
Wavelet has been applying in signal analysising,image processing,model recognizing,computer sense,and so on, more and more generally. Researches of biorthogonal wavelet in this(wavelet) field are being gone on.Some reseachers having gathered several such filters and relative wavelet ,but the application effect is not very good and the application fields is not so wide .The construction method of biorthogonal wavelet presented has great effect and large generality,which can be used not only in the fields above mentioned,but also in the fields of maths,communication,earthquake,chemistry,and so on.
Wavelet has been applying in signal analysising,image processing,model recognizing,computer sense,and so on, more and more generally. Researches of biorthogonal wavelet in this(wavelet) field are being gone on.Some reseachers having gathered several such filters and relative wavelet ,but the application effect is not very good and the application fields is not so wide .The construction method of biorthogonal wavelet presented has great effect and large generality,which can be used not only in the fields above mentioned,but also in the fields of maths,communication,earthquake,chemistry,and so on.
引文
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[4] Cohen A, Daubechies I, Vial P. W avelets on the interval and fast w avelet transform s [ J]. App l. Comp ut. Harm on. Anal.,1993,1:54～81.
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[9] W ickerhause M V. Adapted w avelet analysis from theory to softw are [ M ]. New York: S I A M,1994.442～462.
[10] Vaidyanathan P P, Huong P Q. Lattice structures for optim aldesign and robustim plem ention oftw ochannelperfect- reconstruction Q M F banks [ J]. I E E E Trans. on A S S P,1997,36(1):81～94.
[11] Geronim o J S. Fractalfunctions and w avelet expensions based on several scaling functions [ J]. J. Approx . Theory,1996,78:373～401.
[12] Zhou Dingxuan. Multivariate orthom orm albases of w avelets [ J]. M athem atical Research & Exp osition,1992,12(2):179～182.
[13] Argoul F, Arneodo A , Elezgaray J, et al. W avelet analysis of the selfsim ilarity of diffusion- lim ited aggregatesand electrodeposition clusters [ J]. Phys. Rev( A),1990,41(10):5527～5560.
[2] Strang G. Creating and com paring w avelets [ A]. W atson G A. Num erical Analysis, Mitchell Birthday Volum e A R[ C]. Singapore: World Scientic,1996.200～212..
[3] Cohen A, Daubechies I, Feauveau J C. Biorthogonalbases of com pactly supported w avelets [ J]. Com m un. Pure Appl. M ath.,1992,45:485～560.
[4] Cohen A, Daubechies I, Vial P. W avelets on the interval and fast w avelet transform s [ J]. App l. Comp ut. Harm on. Anal.,1993,1:54～81.
[5] Donoho D, Johnstone I M , Kerkyacharianm G et al. W avelet shrinkage: Asym ptopia? [ J]. J. R. Stat. Soc. B,1996,57:301～369.
[6] Quak E. Trigonom etric w avelets for Herm ite interpolation [ J]. Mathenatics of Comp utation,1996,65(214):683～722.
[7] Law ton W , Lee S L, Shen Z W . An Algorithm for m atrix extension and w avelet construction [ J]. Mathem atics of Comp utation,1996,65(214):723～727.
[8] Chen H L. Periodic orthom orm al quasiw avelet bases [ J]. Chinese Science Bulletin,1996,41(7): 552～554.
[9] W ickerhause M V. Adapted w avelet analysis from theory to softw are [ M ]. New York: S I A M,1994.442～462.
[10] Vaidyanathan P P, Huong P Q. Lattice structures for optim aldesign and robustim plem ention oftw ochannelperfect- reconstruction Q M F banks [ J]. I E E E Trans. on A S S P,1997,36(1):81～94.
[11] Geronim o J S. Fractalfunctions and w avelet expensions based on several scaling functions [ J]. J. Approx . Theory,1996,78:373～401.
[12] Zhou Dingxuan. Multivariate orthom orm albases of w avelets [ J]. M athem atical Research & Exp osition,1992,12(2):179～182.
[13] Argoul F, Arneodo A , Elezgaray J, et al. W avelet analysis of the selfsim ilarity of diffusion- lim ited aggregatesand electrodeposition clusters [ J]. Phys. Rev( A),1990,41(10):5527～5560.
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