The Orthogonality Properties of Vector-Valued Two-dimensional Wavelet Packets with an Integer Dilation Factor

Wavelet analysis has been developing a popular mathematical branch for twenty years. In this paper the notion of orthogonal vector-valued two-dimensional wavelet packets, which is a generalization of uni-wavelet packets, is introduced. Their orthogonality properties are discussed by virtue of time-frequency analysis method, operator theory and matrix theory. Orthogonality formulas are established. Three orthonormal basis of L
²
(R
²
,C
^u
) is established from these orthogonal vector-valued wavelet packets.