Convergence of Riemannian sums of inverse wavelet transforms |
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Authors: | SUN XuDong & SUN WenChang |
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Affiliation: | SUN XuDong & SUN WenChang* Department of Mathematics and LPMC,Nankai University,Tianjin 300071,China |
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Abstract: | We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones. |
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Keywords: | wavelet frames wavelet transforms Riemannian sums |
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