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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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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
Consistent Sampling and Signal Recovery
"... Abstract—An attractive formulation of the sampling problem is based on the principle of a consistent signal reconstruction. The requirement is that the reconstructed signal is indistinguishable from the input in the sense that it yields the exact same measurements. Such a system can be interpreted a ..."
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Cited by 19 (2 self)
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Abstract—An attractive formulation of the sampling problem is based on the principle of a consistent signal reconstruction. The requirement is that the reconstructed signal is indistinguishable from the input in the sense that it yields the exact same measurements. Such a system can be interpreted
Adaptive sensing for sparse signal recovery
 Proc. IEEE 13th Digital Sig. Proc./5th Sig. Proc. Education Workshop
, 2009
"... The theory of compressed sensing shows that sparse signals in highdimensional spaces can be recovered from a relatively small number of samples in the form of random projections. However, in severely resourceconstrained settings even CS techniques may fail, and thus, a less aggressive goal of part ..."
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Cited by 19 (6 self)
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of partial signal recovery is reasonable. This paper describes a simple dataadaptive procedure that efficiently utilizes information from previous observations to focus subsequent measurements into subspaces that are increasingly likely to contain true signal components. The procedure is analyzed in a
Signal Recovery on Incoherent Manifolds
"... Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a highdimensional ambient space. We introduce SPIN, a firstorder projected gradient method to recover the signal com ..."
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Cited by 7 (1 self)
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components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN
Greedy signal recovery review
 Proc. 42nd Asilomar Conference on Signals, Systems, and Computers
, 2008
"... Abstract. The two major approaches to sparse recovery are L1minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform gu ..."
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Cited by 7 (0 self)
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Abstract. The two major approaches to sparse recovery are L1minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform
StructureBlind Signal Recovery
"... Abstract We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspec ..."
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Abstract We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set
SIGNAL RECOVERY AND FRAMES THAT ARE ROBUST TO ERASURE
"... Abstract. We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy. This follows from a result in random matrix theory. ..."
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. We also give an application of the operator Khintchine inequality in the setting of signal recovery when the signal is a matrix with a sparse representation. 1. Introduction and
SPARSE SIGNAL RECOVERY WITH SIDE INFORMATION
"... The paper proposes an algorithm for signal recovery with side information. It is assumed that the decoder has a priori knowledge about the sparse source signal in the form of side information, that can be used to estimate positions of significant elements in the source. The proposed iterative algori ..."
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Cited by 3 (0 self)
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The paper proposes an algorithm for signal recovery with side information. It is assumed that the decoder has a priori knowledge about the sparse source signal in the form of side information, that can be used to estimate positions of significant elements in the source. The proposed iterative
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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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
Results 11  20
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3,921