Title :
Uniform Convergence of Tensor Product Wavelet Series
Author :
Leng, Jin-Song ; Huang, Ting-Zhu ; Liao, Zhi-wu
Author_Institution :
Fac. of Appl. Math., Univ. of Electron. Sci. & Technol. of China, Chengdu
Abstract :
Multi-dimensional wavelet series have become powerful tool of image processing. Via constructing a compactly support domain, an expression constituted by partial sums and truncated term of wavelet expansions of a given multi-dimensional distribution f is obtained. It´s easy for helping us to study uniform convergence of tensor product wavelet series. In fact, we show wavelet expansions are convergent uniformly if the given function f belonging to the Sobolev space Hs with s ges 1/2 by using the result
Keywords :
Fourier transforms; convergence; image processing; series (mathematics); tensors; wavelet transforms; Sobolev space; image processing; multidimensional distribution; multidimensional wavelet series; tensor product wavelet series; uniform convergence; wavelet expansions; Convergence; Cybernetics; Fourier transforms; Image converters; Image processing; Machine learning; Mathematics; Multidimensional signal processing; Multiresolution analysis; Tensile stress; Wavelet analysis; Wavelet domain; Orthogonal wavelet basis; m-dimensional multiresolution analysis; m-dimensional tensor product space;
Conference_Titel :
Machine Learning and Cybernetics, 2006 International Conference on
Conference_Location :
Dalian, China
Print_ISBN :
1-4244-0061-9
DOI :
10.1109/ICMLC.2006.258873
