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THRESHOLDING ESTIMATORS FOR MINIMAX RESTORATION AND
"... Inverting the distortion of signals and images in presence of additive noise is often numerically unstable. To solve these illposed inverse problems, we study linear and nonlinear diagonal estimators in an orthogonal basis. General conditions are given to build nearly minimax optimal estimators wi ..."
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Inverting the distortion of signals and images in presence of additive noise is often numerically unstable. To solve these illposed inverse problems, we study linear and nonlinear diagonal estimators in an orthogonal basis. General conditions are given to build nearly minimax optimal estimators
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
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Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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where both are uniformly convex. The wide applicability of the proposed algorithm is demonstrated on several imaging problems such as image denoising, image deconvolution, image inpainting, motion estimation and image segmentation. 1
An EM Algorithm for WaveletBased Image Restoration
, 2002
"... This paper introduces an expectationmaximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with lowcomplexity, expressed in terms of the wavelet coecients, taking a ..."
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Cited by 351 (23 self)
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This paper introduces an expectationmaximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with lowcomplexity, expressed in terms of the wavelet coecients, taking
Thresholding Estimators for Linear Inverse Problems and Deconvolutions
, 2003
"... Thresholding algorithms in an orthonormal basis are studied to estimate noisy discrete signals degraded by a linear operator whose inverse is not bounded. For signals in a set Theta, sufficient conditions are established on the basis to obtain a maximum risk with minimax rates of convergence. Deconv ..."
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Cited by 45 (2 self)
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to be asymptotically equivalent to the minimax risk over bounded variation signals. This thresholding estimator is used to restore blurred satellite images.
Thresholding Estimators for Linear Inverse Problems and Deconvolutions
"... Thresholding algorithms in an orthonormal basis are studied to estimate noisy discrete signals degraded by a linear operator whose inverse is not bounded. For signals in a set Θ, sufficient conditions are established on the basis to obtain a maximum risk with minimax rates of convergence. Deconvolu ..."
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Thresholding algorithms in an orthonormal basis are studied to estimate noisy discrete signals degraded by a linear operator whose inverse is not bounded. For signals in a set Θ, sufficient conditions are established on the basis to obtain a maximum risk with minimax rates of convergence. Deconvolutions
Deconvolution by thresholding in mirror wavelet bases
 IEEE Transactions on Image Processing
, 2003
"... The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly subopti ..."
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Cited by 20 (0 self)
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The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub
Results 1  10
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4,783