一类四元数小波包的构造

On the construction of a class of quaternion-valued wavelet packets

实值二维信号可以用四元数来表示,因此,四元数的尺度函数和小波的构造就成为分析二维信号的关键.引入了四元数小波包的概念,并且借助于四元数多分辨分析和四元数尺度函数和四元数小波函数的概念和若干公式,给出并构造了一类四元数正交小波包的构造方法,得到了四元数正交小波包的3个正交性公式,最后,利用四元数正交小波包给出了L2(R,C2×2)空间的新的正交基.

As it is known to all that real two-dimensional signals can be represented by quaternion,so it is important for analyzing two-dimensional signals to constructing quaternion-valued scaling function and quaternionvalued wavelet. In this paper, the notion of quaternion-valued wavelet packet is introduced. And by virtue of the notion of quaternion-valued scaling function and wavelet function and several formulas given by M.Bahli, we offer a procedure for constructing a class of quaternion-valued wavelet packet. Three orthogonality formula concerning the quaternion-valued wavelet packet are investigated. Finally, new orthogonal bases of L2 （R, C^2 × 2） are constructed from these quaternion-valued wavelet packet.