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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.