Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation
In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.
X. X. Tian and A. L. Huo, "Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation", Applied Mechanics and Materials, Vols. 20-23, pp. 1053-1059, 2010