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Approximating RateDistortion Graphs of Individual Data: Experiments in Lossy
"... Abstract — Classical ratedistortion theory requires knowledge of an elusive source distribution. Instead, we analyze ratedistortion properties of individual objects using the recently developed algorithmic ratedistortion theory. The latter is based on the noncomputable notion of Kolmogorov comple ..."
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complexity. To apply the theory we approximate the Kolmogorov complexity by standard data compression techniques, and perform a number of experiments with lossy compression and denoising of objects from different domains. We also introduce a natural generalization to lossy compression with side information
Approximating ratedistortion graphs of individual data
 Experiments in lossy compression and denoising,” IEEE Trans. Comput., Submitted. Also: Arxiv preprint cs.IT/0609121
, 2006
"... Abstract—Classical ratedistortion theory requires specifying a source distribution. Instead, we analyze ratedistortion properties of individual objects using the recently developed algorithmic ratedistortion theory. The latter is based on the noncomputable notion of Kolmogorov complexity. To appl ..."
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Cited by 16 (2 self)
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. To apply the theory we approximate the Kolmogorov complexity by standard data compression techniques, and perform a number of experiments with lossy compression and denoising of objects from different domains. We also introduce a natural generalization to lossy compression with side information
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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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 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 coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
The curvelet transform for image denoising
 IEEE TRANS. IMAGE PROCESS
, 2002
"... We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform [2] and the curvelet transform [6], [5]. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A cen ..."
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Cited by 396 (40 self)
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We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform [2] and the curvelet transform [6], [5]. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A
On Algorithmic RateDistortion Function
"... Abstract — We develop ratedistortion theory in the Kolmogorov complexity setting. This is a theory of lossy compression of individual data objects, using the computable regularities of the data. I. ..."
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Cited by 1 (0 self)
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Abstract — We develop ratedistortion theory in the Kolmogorov complexity setting. This is a theory of lossy compression of individual data objects, using the computable regularities of the data. I.
Algorithmic ratedistortion theory
 IEEE Trans. Inform. Th
, 2004
"... We propose and develop ratedistortion theory in the Kolmogorov complexity setting. This gives the ultimate limits of lossy compression of individual data objects, taking all effective regularities of the data into account. 1 ..."
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Cited by 3 (0 self)
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We propose and develop ratedistortion theory in the Kolmogorov complexity setting. This gives the ultimate limits of lossy compression of individual data objects, taking all effective regularities of the data into account. 1
Adaptive Wavelet Thresholding for Image Denoising and Compression
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2000
"... The first part of this paper proposes an adaptive, datadriven threshold for image denoising via wavelet softthresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing ..."
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Cited by 351 (4 self)
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The first part of this paper proposes an adaptive, datadriven threshold for image denoising via wavelet softthresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing
Image denoising by sparse 3D transformdomain collaborative filtering
 IEEE TRANS. IMAGE PROCESS
, 2007
"... We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call “groups.” Collaborative filtering is a special procedure d ..."
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Cited by 422 (32 self)
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We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call “groups.” Collaborative filtering is a special procedure
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done
Results 1  10
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