1. Convergence of wavelet thresholding estimators of differential operators
- Author
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Chen, Di-Rong and Meng, Hongtao
- Subjects
- *
WAVELETS (Mathematics) , *MATHEMATICS , *DIFFERENTIAL operators , *DIFFERENTIAL equations - Abstract
Abstract: Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given signal. The shrinkage method is applied in different areas, including data compression, signal processing and statistics. The almost everywhere convergence of resulting wavelet series has been established in [T. Tao, On the almost everywhere convergence of wavelet summation methods, Appl. Comput. Harmon. Anal. 3 (1996) 384–387] and [T. Tao, B. Vidakovic, Almost everywhere behavior of general wavelet shrinkage operators, Appl. Comput. Harmon. Anal. 9 (2000) 72–82]. With a representation of in terms of wavelet coefficients of f, we are interested in considering the influence of wavelet thresholding to f on its derivative . In this paper, for the representation of differential operators in nonstandard form, we establish the almost everywhere convergence of estimators as threshold tends to zero. [Copyright &y& Elsevier]
- Published
- 2008
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