Simultaneous Wavelet Deconvolution in Periodic Setting |
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Authors: | DANIELA DE CANDITIIS MARIANNA PENSKY |
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Institution: | Istituto per le Applicazioni del Calcolo 'M. Picone'; Department of Mathematics, University of Central Florida |
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Abstract: | Abstract. The paper proposes a method of deconvolution in a periodic setting which combines two important ideas, the fast wavelet and Fourier transform-based estimation procedure of Johnstone et al . J. Roy. Statist. Soc. Ser. B 66 (2004) 547] and the multichannel system technique proposed by Casey and Walnut SIAM Rev . 36 (1994) 537]. An unknown function is estimated by a wavelet series where the empirical wavelet coefficients are filtered in an adapting non-linear fashion. It is shown theoretically that the estimator achieves optimal convergence rate in a wide range of Besov spaces. The procedure allows to reduce the ill-posedness of the problem especially in the case of non-smooth blurring functions such as boxcar functions: it is proved that additions of extra channels improve convergence rate of the estimator. Theoretical study is supplemented by an extensive set of small-sample simulation experiments demonstrating high-quality performance of the proposed method. |
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Keywords: | deconvolution Meyer wavelets multichannel system non-parametric regression |
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