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In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector wavelets are introduced. The existence of biorthogonal finitely supported vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is discussed. A procedure for designing a class of biorthogonal vector-valued finitely supported wavelet functions is proposed...
The notion of vector-valued wavelets associated with an orthogonal vector-valued scaling function with 3-scale is introduced. The existence of orthogonal vector-valued wavelets is discussed and a necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a class of orthogonal...
In this paper, the notion of univariate orthogonal wavelet packets is generalized. First, the definition of nonseparable biorthogonal bivariate wavelet packets is given and a procedure for constructing them is presented. Next, the biorthogonality properties of biorthogonal bivariate wavelet packets is investigated.
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