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Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
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Cited by 460 (22 self)
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Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes
Efficient Learning and Inference of Sparse Overcomplete Representations
"... Sparse overcomplete representations are useful in many vision applications, such as feature extraction [7], recognition [6], denoising, and inpainting of natural images [2]. Many such algorithms have focused on learning a dictionary of basis functions such that any image patch can be reconstructed a ..."
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Sparse overcomplete representations are useful in many vision applications, such as feature extraction [7], recognition [6], denoising, and inpainting of natural images [2]. Many such algorithms have focused on learning a dictionary of basis functions such that any image patch can be reconstructed
Energybased models for sparse overcomplete representations
 Journal of Machine Learning Research
, 2003
"... We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption resul ..."
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Cited by 69 (15 self)
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We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption
Further results on stable recovery of sparse overcomplete representations in the presence of noise
, 2009
"... Sparse overcomplete representations have attracted much interest recently for their applications to signal processing. In a recent work, Donoho, Elad, and Temlyakov [12] showed that, assuming sufficient sparsity of the ideal underlying signal and approximate orthogonality of the overcomplete dictio ..."
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Cited by 6 (1 self)
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Sparse overcomplete representations have attracted much interest recently for their applications to signal processing. In a recent work, Donoho, Elad, and Temlyakov [12] showed that, assuming sufficient sparsity of the ideal underlying signal and approximate orthogonality of the overcomplete
Learning sparse, overcomplete representations of timevarying natural images
 in Proceedings of the IEEE International Conference on Image Processing
, 2003
"... I show how to adapt an overcomplete dictionary of spacetime functions so as to represent timevarying natural images with maximum sparsity. The basis functions are considered as part of a probabilistic model of image sequences, with a sparse prior imposed over the coefficients. Learning is accomplis ..."
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Cited by 27 (0 self)
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I show how to adapt an overcomplete dictionary of spacetime functions so as to represent timevarying natural images with maximum sparsity. The basis functions are considered as part of a probabilistic model of image sequences, with a sparse prior imposed over the coefficients. Learning
Sparse Overcomplete Representations for Efficient Identification of Power Line Outages
"... AbstractFast and accurate unveiling of powerline outages is of paramount importance not only for preventing faults that may lead to blackouts, but also for routine monitoring and control tasks of the smart grid, including state estimation and optimal power flow. Existing approaches are either cha ..."
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number of lines, the novel approach relies on reformulating the DC linear power flow model as a sparse overcomplete expansion and leveraging contemporary advances in compressive sampling and variable selection. This sparse representation can also be extended to incorporate available information
Estimation of the optimal neural features in the context of sparse overcomplete representations
, 2005
"... One of the critical functions of the brain is to determine what is going on in the real world from neuronal spiking patterns. This is called the “decoding ” problem, in contrast to the “encoding” problem where we try to estimate the neural responses to known stimuli. Neuroscientists have long tried ..."
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One of the critical functions of the brain is to determine what is going on in the real world from neuronal spiking patterns. This is called the “decoding ” problem, in contrast to the “encoding” problem where we try to estimate the neural responses to known stimuli. Neuroscientists have long tried to address these problems, and we made some progress in solving the decoding problem
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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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
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 958 (9 self)
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field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex
Results 1  10
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67,392