Inversion of noisy Radon transform by SVD based needlet (2008)
Kerkyacharian, Gérard, Kyriazis, George, Le Pennec, Erwan, Petrushev, Pencho, Picard, Dominique
A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis....
Inversion of noisy Radon transform by SVD based needlet (2008)
Kerkyacharian, Gérard, Kyriazis, George, Le Pennec, Erwan, Petrushev, Pencho, Picard, Dominique
A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis....
Inversion of noisy Radon transform by SVD based needlet (2008)
Kerkyacharian, Gérard, Kyriazis, George, Pennec, Erwan Le, Petrushev, Pencho, Picard, Dominique
A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis....
Needlet algorithms for estimation in inverse problems (2007)
Kerkyacharian, Gérard, Petrushev, Pencho, Picard, Dominique, Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to...
NEED-VD: a second-generation wavelet algorithm for estimation in inverse problems (2006)
Kerkyacharian, Gérard, Petrushev, Pencho, Picard, Dominique, Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to...
NEED-VD: a second-generation wavelet algorithm for estimation in inverse problems (2006)
Kerkyacharian, Gérard, Petrushev, Pencho, Picard, Dominique, Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to...
NEED-VD: a second-generation wavelet algorithm for estimation in inverse problems (2006)
Kerkyacharian, Gérard, Petrushev, Pencho, Picard, Dominique, Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to...
NEED-VD: a second-generation wavelet algorithm for estimation in inverse problems (2006)
Kerkyacharian, Gérard, Petrushev, Pencho, Picard, Dominique, Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to...
High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus (2006)
Baldi, Paolo, Kerkyacharian, Gérard, Marinucci, Domenico, Picard, Dominique
We prove a CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to...
High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus (2006)
Baldi, Paolo, Kerkyacharian, Gérard, Marinucci, Domenico, Picard, Dominique
We prove a CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to...
High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus (2006)
Baldi, Paolo, Kerkyacharian, Gérard, Marinucci, Domenico, Picard, Dominique
We prove a CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to...
High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus (2006)
Baldi, Paolo, Kerkyacharian, Gérard, Marinucci, Domenico, Picard, Dominique
We prove a CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to...
Regression in random design and warped wavelets (2004)
Kerkyacharian, Gérard, Picard, Dominique
We consider the problem of estimating an unknown function f in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis...
Adaptive boxcar deconvolution on full Lebesgue measure sets (2004)
Kerkyacharian, Gérard, Picard, Dominique, Raimondo, Marc
We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval $(-a,a)$. In a recent paper \citet{jkpr04} have...
Adaptive boxcar deconvolution on full Lebesgue measure sets (2004)
Kerkyacharian, Gérard, Picard, Dominique, Raimondo, Marc
We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval $(-a,a)$. In a recent paper \citet{jkpr04} have...
Adaptive boxcar deconvolution on full Lebesgue measure sets (2004)
Kerkyacharian, Gérard, Picard, Dominique, Raimondo, Marc
We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval $(-a,a)$. In a recent paper \citet{jkpr04} have...
Adaptive boxcar deconvolution on full Lebesgue measure sets (2004)
Kerkyacharian, Gérard, Picard, Dominique, Raimondo, Marc
We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval $(-a,a)$. In a recent paper \citet{jkpr04} have...
Kerkyacharian, Gérard, Picard, Dominique
We discuss a new way of evaluating the performance of a statistical estimation procedure. This consists of investigating the maximal set where a given procedure has a given rate of convergence....
Thresholding algorithms, maxisets and well-concentrated bases (2000)
Kerkyacharian, Gérard, Picard, Dominique
The aim of this paper la to synthetically analyse the performances of thresholding and wavelet estimation methods. In this connection, it la useful to describe the maxlmal sets where these methods...
Thresholding algorithms, maxisets and well-concentrated bases (2000)
Kerkyacharian, Gérard, Picard, Dominique
The aim of this paper la to synthetically analyse the performances of thresholding and wavelet estimation methods. In this connection, it la useful to describe the maxlmal sets where these methods...
Block threshold rules for curve estimation using kernel and wavelet methods (1998)
Hall, Peter, Kerkyacharian, Gérard, Picard, Dominique
Motivated by recently developed threshold rules for wavelet estimators, we suggest threshold methods for general kernel density estimators, including those of classical Rosenblatt–Parzen type....
Estimating nonquadratic functionals of a density using Haar wavelets (1996)
Kerkyacharian, Gérard, Picard, Dominique
Z.Consider the problem of estimating $\int \Phi(f)$, where $\Phi$ is a smooth function and f is a density with given order of regularity s. Special attention is paid to the case $\Phi(t) = t^3$. It...
Density estimation by wavelet thresholding (1996)
Donoho, David L., Johnstone, Iain M., Kerkyacharian, Gérard, Picard, Dominique
Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients....
Wavelet deconvolution in a periodic setting
Iain M. Johnstone, Gérard Kerkyacharian, Dominique Picard, Marc Raimondo
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...
Thresholding algorithms, maxisets and well-concentrated bases
Gérard Kerkyacharian, Dominique Picard, Lucien Birgé, Peter Hall, Oleg Lepski, Enno Mammen, ...
Approximation methods, Besov spaces, denoising, minimax rate of convergence, non parametric estimation, oracle inequalities, saturation spaces, wavelet thresholding, 62G05, 62G07, 62G20,