CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Needell, Deanna; Tropp, Joel A.

doi:10.1016/j.acha.2008.07.002

Cited by 3,758 publications

(3,182 citation statements)

References 30 publications

(60 reference statements)

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“…IP address: 52.183.12.225, on 11 Apr 2019 at 13:59:57, subject to the Cambridge Core of exact recovery of sparse signals and the Lebesgue-type inequalities for these algorithms: the regularized orthogonal matching pursuit (see [12]), the compressive sampling matching pursuit (CoSaMP; see [11]), and the subspace pursuit (SP; see [1]). The OMP is simpler than the CoSaMP and the SP; however, at the time of invention of the CoSaMP and the SP these algorithms provided exact recovery of sparse signals and the Lebesgue-type inequalities for dictionaries satisfying the restricted isometry property (RIP) (see [11] and [1]). The corresponding results for the OMP were not known at that time.…”

Section: Discussionmentioning

confidence: 99%

Sparse Approximation and Recovery by Greedy Algorithms in Banach Spaces

Temlyakov

2014

Forum math. Sigma

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We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the weak Chebyshev greedy algorithm (WCGA), a generalization of the weak orthogonal matching pursuit to the case of a Banach space. The main novelty of these results is a Banach space setting instead of a Hilbert space setting. The results are proved for redundant dictionaries satisfying certain conditions. Then we apply these general results to the case of bases. In particular, we prove that the WCGA provides almost optimal sparse approximation for the trigonometric system in L p , 2 p < ∞.

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Section: Discussionmentioning

confidence: 99%

Sparse Approximation and Recovery by Greedy Algorithms in Banach Spaces

Temlyakov

2014

Forum math. Sigma

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“…Then the following experiments are using the same settings, where the model hyperparameters for the priors in CluSS are set as Then several experiments considered widely in CS literatures are implemented via CluSS, and comparisons are made to the state-of-the-art CS algorithms, respectively, Basis Pursuit (BP) [31], CoSaMP [32], Block-CoSaMP [10], (K, S)-sparse recovery algorithm via Dynamic Programming (Block-DP) [12] and Bayesian Compressive Sensing (BCS) [21]. Without special explanation, the sensing matrix Φ is constructed randomly as in the seminal work [2], i.e., entries are drawn independently from Gaussian distribution…”

Section: Methodsmentioning

confidence: 99%

Bayesian compressive sensing for cluster structured sparse signals

et al. 2012

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In traditional framework of Compressive Sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called modelbased compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian Compressive Sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically -prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.

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“…Thus it is an alternative choice in high dynamic environment where it is difficult, if not impossible, to obtain enough number of snapshots for the fixed DOAs. The representative compressive sensing algorithms include convex relaxation algorithms [6,7] and greedy algorithms [8,9]. It has been proved that the compressive sensing algorithms can accurately recover the sparse signal under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

HIGH-DYNAMIC DOA ESTIMATION BASED ON WEIGHTED L<sub>1</sub> MINIMIZATION

Wang¹,

Wu²

2013

PIER C

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Abstract-In high dynamic environment, due to the rapid relative movement between receiver and transmitter, the DOA (Direction of Arrival) of signals will change even between two consecutive snapshots. Thus, covariance-based DOA estimation algorithms are ineffective. Compressive sensing algorithms, as a kind of novel DOA estimation algorithms, are still effective with only one snapshot. At the same time, it is noted that the DOA changing is limited by relative moving speed and distance between receiver and transmitter. In this paper, a DOA tracking algorithm based on weighted L 1 minimization is proposed which utilizing the DOA changing scope between two consecutive snapshots as a prior to improve the tracking performance. Different from other multiple snapshots compressive sensing algorithms which assumed fixed DOA among multiple consecutive snapshots, the proposed algorithm takes into account the DOA changing among different snapshots. The simulation results demonstrate the advantages of the proposed algorithm.

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CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Cited by 3,758 publications

References 30 publications

Sparse Approximation and Recovery by Greedy Algorithms in Banach Spaces

Sparse Approximation and Recovery by Greedy Algorithms in Banach Spaces

Bayesian compressive sensing for cluster structured sparse signals

HIGH-DYNAMIC DOA ESTIMATION BASED ON WEIGHTED L<sub>1</sub> MINIMIZATION

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