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In this work, the notion of biorthogonal two-direction compactly supported wavelet packets with four-scale dilation is introduced. We develop a new method for designing two-direction biorthogonal wavelet packets and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. The decomposition relationship is established. Lastly, two new Riesz bases...
The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of L2...
Wavelet analysis has been developing a widely used mathematical branch for twenty years. In this work, the notion of orthogonal vector-valued wavelet packets in higher dimensions is introduced. A feasible procedure for designing them is presented. Their properties are characterized by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established.
Wavelet analysis has become a popular subject in scientific research in the past twenty years. Nowadays, it has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this article, the notion of orthogonal vector-valued wavelet packets with 3Is-dilation matrix in higher dimensions is introduced. A procedure for constructing them...
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