Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of ...Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.展开更多
In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer di...In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer dilation factor m ≥2. The n-d GMRA is discussed in orthogonal and bi-orthogonal cases. Then the optimal m-band wavelets are applied in processing the image datasets of the human body slices. The efficiency and superiority of the algorithm can be seen from the processing results.展开更多
基金Project supported by the Natural Science Foundation of Guangdong Province (Nos.032038, 05008289, 06105648) the Doctoral Foundation of Guangdong Province (No.04300917)
文摘Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.
基金National High-Tech Research and Development Plan(2001AA231031)National Key Basic Research Plan(G1998030608)National Special R&D Plan for Olympic Games(2001BAg04B08).
文摘In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer dilation factor m ≥2. The n-d GMRA is discussed in orthogonal and bi-orthogonal cases. Then the optimal m-band wavelets are applied in processing the image datasets of the human body slices. The efficiency and superiority of the algorithm can be seen from the processing results.
