2-尺度三维八向双正交小波包及其性质

2-scale Three-dimensional Eight-direction Biorthogonal Wavelet Packets and Their Properties

小波包分解由于具有很强的时频局域化分解能力而得到广泛应用。在a-尺度三维八向小波函数构造算法分析研究的基础上,给出了2-尺度三维八向双正交小波包的定义,并对其做Fourier变换,得到了与其相对应的8×8的对称矩阵Γ,最后探究并证明了2-尺度三维八向双正交小波包的正交性质,为进一步研究高维度双正交小波包提供参考和借鉴。

Wavelet packet decomposition is widely used because of its strong ability of time-frequency local-ized decomposition.On the basis of the analysis and research of the construction algorithm of a-scale three-dimen-sional eight-way wavelet function,we give the definition of the 2-scale three-dimensional eight-direction biorthogo-nal wavelet packets,and Fourier transform them,and obtain the corresponding[8×8]symmetric matrix[Γ].Final-ly,the biorthogonal properties of the 2-scale three-dimensional eight-direction biorthogonal wavelet packets are ex-plored and proved.It provides reference for further study of high dimensional biorthogonal wavelet packets.