The Features of Biorthogonal Binary Poly-scale Wavelet Packs in Bidimensional Function Space

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable separation approach. Three orthogonality formulas regarding these wavelet wraps are obtained. Moreover, it is shown how to draw new orthonormal bases of space L 2(R 2) from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.