Wavelet deconvolution in a periodic setting
Identifieur interne : 00A852 ( Main/Exploration ); précédent : 00A851; suivant : 00A853Wavelet deconvolution in a periodic setting
Auteurs : Iain M. Johnstone [États-Unis] ; Gérard Kerkyacharian [France] ; Dominique Picard [France] ; Marc Raimondo [Australie]Source :
- Journal of the Royal Statistical Society: Series B (Statistical Methodology) [ 1369-7412 ] ; 2004-08.
Descripteurs français
- Pascal (Inist)
- Wicri :
- topic : Méthode statistique, Niveau sonore, Télédétection.
English descriptors
- KwdEn :
- Abramovich, Algorithm, Asymptotic approximation, Asymptotic theory, Besov, Besov spaces, Blur, Boxcar, Boxcar blur, Candidate vaguelettes, Convergence rate, Convolution, Deconvolution, Deconvolution problems, Dense case, Donoho, Error estimation, Estimator, Fast Fourier transformation, Fourier, Fourier domain, Fractions algorithm, High noise scenario, Ieee trans, Inequality, Irrational number, Irrational numbers, Johnstone, Kerkyacharian, Kernel method, Lidar, Lidar signal, Lidar signals, Loss function, Lower bounds, Lp approximation, Maximum level, Medium noise, Medium noise scenario, Meyer wavelet, Multiresolution analysis, Neelamani, Nest scale, Noise level, Noise scenario, Periodized, Picard, Raimondo, Rational numbers, Real number, Regularization, Regularization parameter, Remote sensing, Scenario, Silverman, Smooth blur, Stanford, Stanford university, Statistical method, System response functions, Target function, Temlyakov property, Thresholding, Unknown function, Wavelet, Wavelet deconvolution, Wavelet deconvolution method, Wavelet transformation, White noise.
- Teeft :
- Abramovich, Algorithm, Asymptotic theory, Besov, Besov spaces, Blur, Boxcar, Boxcar blur, Candidate vaguelettes, Convolution, Deconvolution, Deconvolution problems, Dense case, Donoho, Estimator, Fourier, Fourier domain, Fractions algorithm, High noise scenario, Ieee trans, Inequality, Irrational number, Irrational numbers, Johnstone, Kerkyacharian, Lidar, Lidar signal, Lidar signals, Lower bounds, Maximum level, Medium noise, Medium noise scenario, Meyer wavelet, Multiresolution analysis, Neelamani, Nest scale, Noise level, Noise scenario, Periodized, Picard, Raimondo, Rational numbers, Real number, Regularization, Regularization parameter, Scenario, Silverman, Smooth blur, Stanford, Stanford university, System response functions, Target function, Temlyakov property, Thresholding, Unknown function, Wavelet, Wavelet deconvolution, Wavelet deconvolution method.
Abstract
Summary. Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise with O{n log (n)2} steps. In the periodic setting, the method applies to most deconvolution problems, including certain ‘boxcar’ kernels, which are important as a model of motion blur, but having poor Fourier characteristics. Asymptotic theory informs the choice of tuning parameters and yields adaptivity properties for the method over a wide class of measures of error and classes of function. The method is tested on simulated light detection and ranging data suggested by underwater remote sensing. Both visual and numerical results show an improvement over competing approaches. Finally, the theory behind our estimation paradigm gives a complete characterization of the ‘maxiset’ of the method: the set of functions where the method attains a near optimal rate of convergence for a variety of Lp loss functions.
Url:
DOI: 10.1111/j.1467-9868.2004.02056.x
Affiliations:
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Le document en format XML
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Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise with O{n log (n)2} steps. In the periodic setting, the method applies to most deconvolution problems, including certain ‘boxcar’ kernels, which are important as a model of motion blur, but having poor Fourier characteristics. Asymptotic theory informs the choice of tuning parameters and yields adaptivity properties for the method over a wide class of measures of error and classes of function. The method is tested on simulated light detection and ranging data suggested by underwater remote sensing. Both visual and numerical results show an improvement over competing approaches. Finally, the theory behind our estimation paradigm gives a complete characterization of the ‘maxiset’ of the method: the set of functions where the method attains a near optimal rate of convergence for a variety of Lp loss functions.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li><li>États-Unis</li></country></list><tree><country name="États-Unis"><noRegion><name sortKey="Johnstone, Iain M" sort="Johnstone, Iain M" uniqKey="Johnstone I" first="Iain M." last="Johnstone">Iain M. Johnstone</name></noRegion></country><country name="France"><noRegion><name sortKey="Kerkyacharian, Gerard" sort="Kerkyacharian, Gerard" uniqKey="Kerkyacharian G" first="Gérard" last="Kerkyacharian">Gérard Kerkyacharian</name></noRegion><name sortKey="Picard, Dominique" sort="Picard, Dominique" uniqKey="Picard D" first="Dominique" last="Picard">Dominique Picard</name></country><country name="Australie"><noRegion><name sortKey="Raimondo, Marc" sort="Raimondo, Marc" uniqKey="Raimondo M" first="Marc" last="Raimondo">Marc Raimondo</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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