An improved RIP-based performance guarantee for sparse signal recovery via simultaneous orthogonal matching pursuit

Li, Haifeng; Ma, Yingbin; Fu, Yuli

doi:10.1016/j.sigpro.2017.09.027

Cited by 11 publications

(9 citation statements)

References 21 publications

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“…Then BOMP with the stopping criterion r k 2 ≤ ε can exactly recover T (see (2)) from (4) in K iterations provided that…”

Section: Resultsmentioning

confidence: 99%

“…Compressed sensing (CS) [1][2][3][4][5] has attracted much attention in recent years. Suppose that we have linear model y = Ax + e, where y ∈ R m is a measurement vector, A ∈ R m×n is a sensing matrix, x ∈ R n is a K-sparse signal (i.e., |supp(x)| ≤ K, where supp(x) = {i : x i = 0} is the support of x and |supp(x)| is the cardinality of supp(x)) and e represents the measurement noise.…”

Section: Introductionmentioning

confidence: 99%

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A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

Wen

2019

IEEE Signal Process. Lett.

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Compressed Sensing (CS) is a signal processing technique which can accurately recover sparse signals from linear measurements with far fewer number of measurements than those required by the classical Shannon-Nyquist theorem. Block sparse signals, i.e., the sparse signals whose nonzero coefficients occur in few blocks, arise from many fields. Block orthogonal matching pursuit (BOMP) is a popular greedy algorithm for recovering block sparse signals due to its high efficiency and effectiveness. By fully using the block sparsity of block sparse signals, BOMP can achieve very good recovery performance. This paper proposes a sufficient condition to ensure that BOMP can exactly recover the support of block K-sparse signals under the noisy case. This condition is better than existing ones.Index Terms-Compressed sensing, sufficient condition, block sparse signal, restricted isometry property.

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“…Then BOMP with the stopping criterion r k 2 ≤ ε can exactly recover T (see (2)) from (4) in K iterations provided that…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

Wen

2019

IEEE Signal Process. Lett.

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“…OMP is an ambitious algorithm (Algorithm 2) since it starts by determining the largest atoms ofα; and it is also based on matching pursuit. Nevertheless, this work does not expose the characteristics of this algorithm since it was not implemented due to the limitations it contains regarding the increase of the number of iterations [20,26,27].…”

Section: Orthogonal Matching Pursuitmentioning

confidence: 99%

“…There are some studies on the behavior of communications networks for the transmission of data obtained from the sensors under the Nyquist-Shannon sampling theory [27,30]. According to the information obtained, it has been possible to detect and classify different types of events on transmission lines in electric power systems.…”

Section: Problem Formulationmentioning

confidence: 99%

Electrical Faults Signals Restoring Based on Compressed Sensing Techniques

Ruiz

Montalvo

2020

Energies

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This research focuses on restoring signals caused by power failures in transmission lines using the basis pursuit, matching pursuit, and orthogonal matching pursuit sensing techniques. The original signal corresponds to the instantaneous current and voltage values of the electrical power system. The heuristic known as brute force is used to find the quasi-optimal number of atoms k in the original signal. Next, we search for the minimum number of samples known as m; this value is necessary to reconstruct the original signal from sparse and random samples. Once the values of k and m have been identified, the signal restoration is performed by sampling sparse and random data at other bus bars of the power electrical system. Basis pursuit allows recovering the original signal from 70% of the random samples of the same signal. The higher the number of samples, the longer the restoration times, approximately 12 s for recovering the entire signal. Matching pursuit allows recovering the same percentage, but with the lowest restoration time. Finally, orthogonal matching pursuit recovers a slightly lower percentage with a higher number of samples with a significant increase in its recovery time. Therefore, for real-time electrical fault signal restoration applications, the best selection will be matching pursuit due to the fact that it presents the lowest machine time, but requires more samples compared with orthogonal matching pursuit. Basis pursuit and orthogonal matching pursuit require fewer sparse and random samples despite the fact that these require a longer processing time for signal recovery. These two techniques can be used to reduce the volume of data that is stored by phasor measurement systems.

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“…The orthogonal matching pursuit algorithm (OMP) [19][20][21], the regularized orthogonal matching pursuit algorithm (ROMP) [22,23], uses each atom and the residual value of the measurement matrix for the inner product. Then, the atom that is most matched with the residual is placed in the support set using some principles.…”

Section: Introductionmentioning

confidence: 99%

A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting

2020

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The signal reconstruction quality has become a critical factor in compressed sensing at present. This paper proposes a matching pursuit algorithm for backtracking regularization based on energy sorting. This algorithm uses energy sorting for secondary atom screening to delete individual wrong atoms through the regularized orthogonal matching pursuit (ROMP) algorithm backtracking. The support set is continuously updated and expanded during each iteration. While the signal energy distribution is not uniform, or the energy distribution is in an extreme state, the reconstructive performance of the ROMP algorithm becomes unstable if the maximum energy is still taken as the selection criterion. The proposed method for the regularized orthogonal matching pursuit algorithm can be adopted to improve those drawbacks in signal reconstruction due to its high reconstruction efficiency. The experimental results show that the algorithm has a proper reconstruction.

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An improved RIP-based performance guarantee for sparse signal recovery via simultaneous orthogonal matching pursuit

Cited by 11 publications

References 21 publications

A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

Electrical Faults Signals Restoring Based on Compressed Sensing Techniques

A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting

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