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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 452 (21 self)
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the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further
Overcomplete Systems of Wavelet and Related Local Bases for Adaptive Signal Representation and Estimation
"... this paper we will discuss the usefulness of overcomplete systems of basis functions, such as wavelets or localized sine and cosine functions, for the adaptive parsimonious representation and estimation of statistical signals which show an inhomogeneous behaviour over time. Typical examples can be f ..."
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this paper we will discuss the usefulness of overcomplete systems of basis functions, such as wavelets or localized sine and cosine functions, for the adaptive parsimonious representation and estimation of statistical signals which show an inhomogeneous behaviour over time. Typical examples can
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2694 (61 self)
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The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods
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 618 (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
A general framework for object detection
 Sixth International Conference on
, 1998
"... This paper presents a general trainable framework for object detection in static images of cluttered scenes. The detection technique we develop is based on a wavelet representation of an object class derived from a statistical analysis of the class instances. By learning an object class in terms of ..."
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Cited by 392 (21 self)
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of a subset of an overcomplete dictionary of wavelet basis functions, we derive a compact representation of an object class which is used as an input to a suppori vector machine classifier. This representation overcomes both the problem of inclass variability and provides a low false detection rate
FUNCTIONAL APPROXIMATIONS USING OVERCOMPLETE BASE SYSTEMS
"... In more detail the Hilbertspace expansions in overcomplete systems (frames) are handled in [Ves01] in context with the theory of pseudoinverse operators. Chen et al. deal in [CDS98] the problem of sparse representation of vectors (signals) in a nitedimensional space using special overcomplete syst ..."
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In more detail the Hilbertspace expansions in overcomplete systems (frames) are handled in [Ves01] in context with the theory of pseudoinverse operators. Chen et al. deal in [CDS98] the problem of sparse representation of vectors (signals) in a nitedimensional space using special overcomplete
A Trainable System for Object Detection
, 2000
"... This paper presents a general, trainable system for object detection in unconstrained, cluttered scenes. The system derives much of its power from a representation that describes an object class in terms of an overcomplete dictionary of local, oriented, multiscale intensity differences between adj ..."
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Cited by 343 (8 self)
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This paper presents a general, trainable system for object detection in unconstrained, cluttered scenes. The system derives much of its power from a representation that describes an object class in terms of an overcomplete dictionary of local, oriented, multiscale intensity differences between
Density, overcompleteness, and localization of frames
 I. THEORY, J. FOURIER ANAL. APPL
, 2005
"... This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in ..."
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Cited by 60 (19 self)
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This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F
Weighted Overcomplete Denoising
, 2003
"... We consider the familiar scenario where independent and identically distributed (i.i.d) noise in an image is removed using a set of overcomplete linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates ( ..."
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Cited by 25 (7 self)
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We consider the familiar scenario where independent and identically distributed (i.i.d) noise in an image is removed using a set of overcomplete linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates
Results 1  10
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6,431