TRANSLATION INVARIANT DECONVOLUTION IN A PERIODIC SETTING

Autor:	Marc Raimondo, David L. Donoho
Rok vydání:	2004
Předmět:	Discrete wavelet transform Applied Mathematics Second-generation wavelet transform Stationary wavelet transform Mathematical analysis Wavelet transform Cascade algorithm Wavelet Signal Processing Deconvolution Algorithm Information Systems Mathematics Meyer wavelet
Zdroj:	International Journal of Wavelets, Multiresolution and Information Processing. :415-431
ISSN:	1793-690X 0219-6913
DOI:	10.1142/s0219691304000640
Popis:	Deconvolution of a noisy signal in a periodic band-limited wavelet basis exhibits visual artifacts in the neighbourhood of discontinuities. This phenomenon is similar to that appearing in denoising with compactly-supported wavelet transforms and can be reduced by "cycle spinning" as in Coifman and Donoho [3]. In this paper we present an algorithm which "cycle-spins" a periodic band-limited wavelet estimator over all circulant shifts in O(n( log (n))2) steps. Our approach is based on a mathematical idea and takes full advantage of the Fast Fourier Transform. A particular feature of our algorithm is to bounce from the Fourier domain (where deconvolution is performed) to the wavelet domain (where denoising is performed). For both smooth and boxcar convolutions observed in white noise, we illustrate the visual and numerical performances of our algorithm in an extensive simulation study of the [Formula: see text] estimator recently proposed by Johnstone, Kerkyacharian, Picard, and Raimondo [8]. All figures presented here are reproducible using the [Formula: see text] software package.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::92d556f0226eacb8eb4c5edd6695588f https://doi.org/10.1142/s0219691304000640 Zobrazit plný text záznamu