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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 935 (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
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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for arbitrary rectangular matrices as well. Our results are connected with the recent literature on compressed sensing, and show that objects other than signals and images can be perfectly reconstructed from very limited information.
Secure spread spectrum watermarking for multimedia
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1997
"... This paper presents a secure (tamperresistant) algorithm for watermarking images, and a methodology for digital watermarking that may be generalized to audio, video, and multimedia data. We advocate that a watermark should be constructed as an independent and identically distributed (i.i.d.) Gauss ..."
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Cited by 1100 (10 self)
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.i.d.) Gaussian random vector that is imperceptibly inserted in a spreadspectrumlike fashion into the perceptually most significant spectral components of the data. We argue that insertion of a watermark under this regime makes the watermark robust to signal processing operations (such as lossy compression
Iterative hard thresholding for compressed sensing
 Appl. Comp. Harm. Anal
"... Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery probl ..."
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Cited by 329 (18 self)
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Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery
Dictionary learning from sparsely corrupted or compressed signals
 In IEEE Intl. Conf. on Acoustics, Speech and Signal Processing
, 2012
"... In this paper, we investigate dictionary learning (DL) from sparsely corrupted or compressed signals. We consider three cases: I) the training signals are corrupted, and the locations of the corruptions are known, II) the locations of the sparse corruptions are unknown, and III) DL from compressed m ..."
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Cited by 5 (2 self)
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In this paper, we investigate dictionary learning (DL) from sparsely corrupted or compressed signals. We consider three cases: I) the training signals are corrupted, and the locations of the corruptions are known, II) the locations of the sparse corruptions are unknown, and III) DL from compressed
Bayesian Compressive Sensing
, 2007
"... The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing ..."
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Cited by 330 (24 self)
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The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing
On Finding Nearest Neighbors in a Set of Compressible Signals
"... Abstract—Numerous applications demand that we manipulate large sets of very highdimensional signals. A simple yet common example is the problem of finding those signals in a database that are closest to a query. In this paper, we tackle this problem by restricting our attention to a special class o ..."
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bounds on the true distance. Validation of this technique on synthetic and real data sets confirms that it could be very well suited to process queries over large databases of compressed signals, avoiding most of the burden of decoding. I.
3D SIGNAL FORMATS AND COMPRESSION Signal Formats
"... • The number of 3D channels worldwide will increase to over 100 by 2015, according to research firm InStat. ..."
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• The number of 3D channels worldwide will increase to over 100 by 2015, according to research firm InStat.
COMPRESSIVE SIGNAL PROCESSINGWITH CIRCULANT SENSING MATRICES
"... Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises of processing the random projections directly, without firs ..."
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Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises of processing the random projections directly, without
A. Random Sampling and Compressive Signal Processing
"... Abstract—In this paper, we study a simple correlationbased strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequencydomain samples. We model the output of this “compressive matched filter ” as a random process whose mean equals ..."
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Abstract—In this paper, we study a simple correlationbased strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequencydomain samples. We model the output of this “compressive matched filter ” as a random process whose mean equals
Results 11  20
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