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Sparse decompositions in ”incoherent” dictionaries
 in Proc. IEEE Intl. Conf. on Image Proc. (ICIP’03
, 2003
"... The purpose of this paper is to generalize a result byDonoho, Huo, Elad and Bruckstein on sparse representations of signals/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for having a ..."
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Cited by 8 (0 self)
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The purpose of this paper is to generalize a result byDonoho, Huo, Elad and Bruckstein on sparse representations of signals/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for hav
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
, 2004
"... In this paper, we develop a robust uncertainty principle for finite signals in C N which states that for nearly all choices T, Ω ⊂ {0,..., N − 1} such that T  + Ω  ≍ (log N) −1/2 · N, there is no signal f supported on T whose discrete Fourier transform ˆ f is supported on Ω. In fact, we can mak ..."
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Cited by 180 (17 self)
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sparse superposition of spikes and complex sinusoids f(s) = � α1(t)δ(s − t) + � α2(ω)e i2πωs/N / √ N. t∈T We show that if a generic signal f has a decomposition (α1, α2) using spike and frequency locations in T and Ω respectively, and obeying ω∈Ω T  + Ω  ≤ Const · (log N) −1/2 · N, then (α1, α2
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M ..."
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Cited by 270 (33 self)
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dimensional source signal s(t). Many natural signals can be sparsely represented in a proper signal dictionary s i (t) = K X k=1 C ik ' k (t) (1.2) The scalar functions ' k
SPARSE DECOMPOSITION OVER NONFULLRANK DICTIONARIES
"... Sparse Decomposition (SD) of a signal on an overcomplete dictionary has recently attracted a lot of interest in signal processing and statistics, because of its potential application in many different areas including Compressive Sensing (CS). However, in the current literature, the dictionary matrix ..."
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Sparse Decomposition (SD) of a signal on an overcomplete dictionary has recently attracted a lot of interest in signal processing and statistics, because of its potential application in many different areas including Compressive Sensing (CS). However, in the current literature, the dictionary
Quaternion Space Sparse Decomposition for Motion Compression and Retrieval
"... Quaternion has become one of the most widely used representations for rotational transformations in 3D graphics for decades. Due to the sparse nature of human motion in both the spatial domain and the temporal domain, an unexplored yet challenging research problem is how to directly represent intrin ..."
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Cited by 2 (0 self)
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intrinsically sparse human motion data in quaternion space. In this paper we propose a novel quaternion space sparse decomposition (QSSD) model that decomposes human rotational motion data into two meaningful parts (namely, the dictionary part and the weight part) with the sparseness constraint on the weight
Sparse Decomposition over MultiComponent Redundant Dictionaries
"... In many applications  such as compression, denoising and source separation  a good and efficient signal representation is characterized by sparsity. This means that many coefficients are close to zero, while only few ones have a nonnegligible amplitude. On the other hand, realworld signals  su ..."
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Cited by 9 (4 self)
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to consider the signal internal structure. As an example that fits this framework, we propose the Weighted Basis Pursuit algorithm, based on the solution of a convex, nonquadratic problem. Results show that this method can provide sparse signal representations and sparse mterms approximations. Moreover
UNCERTAINTY RELATIONS AND SPARSE DECOMPOSITIONS OF ANALOG SIGNALS
"... insight into how sparse a signal x can be represented in an overcomplete dictionary consisting of ~ and '11. It also sheds light on ..."
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insight into how sparse a signal x can be represented in an overcomplete dictionary consisting of ~ and '11. It also sheds light on
A NEW APPROACH FOR SPARSE DECOMPOSITION AND SPARSE SOURCE SEPARATION
"... We introduce a new approach for sparse decomposition, based on a geometrical interpretation of sparsity. By sparse decomposition we mean finding sufficiently sparse solutions of underdetermined linear systems of equations. This will be discussed in the context of Blind Source Separation (BSS). Our p ..."
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Cited by 1 (0 self)
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We introduce a new approach for sparse decomposition, based on a geometrical interpretation of sparsity. By sparse decomposition we mean finding sufficiently sparse solutions of underdetermined linear systems of equations. This will be discussed in the context of Blind Source Separation (BSS). Our
Sparse Decomposition and Modeling of Anatomical Shape Variation
"... on behalf of the LADIS study group Abstract—Recent advances in statistics have spawned powerful methods for regression and data decomposition that promote sparsity, a property that facilitates interpretation of the results. Sparse models use a small subset of the available variables and may perform ..."
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on behalf of the LADIS study group Abstract—Recent advances in statistics have spawned powerful methods for regression and data decomposition that promote sparsity, a property that facilitates interpretation of the results. Sparse models use a small subset of the available variables and may perform
Results 1  10
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