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

Chang, Ling-Hua; Wu, Jwo-Yuh

doi:10.1109/isccsp.2014.6877808

Cited by 32 publications

(64 citation statements)

References 27 publications

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“…where (a) is because P ⊥ T k φ j 2 ≤ φ j 2 = 1 for each of j ∈ Ω \ T . Clearly, the bound in (22) is tighter than that in (21) by the factor of 2 √ 3 . ii) In [6], by putting…”

Section: Lemma 3 ([2 Theorem 1]mentioning

confidence: 97%

A Near-Optimal Condition for Exact Sparse Recovery with Orthogonal Least Squares

Kim

Shim

2019

2019 IEEE/CIC International Conference on Communications in China (ICCC)

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The orthogonal least squares (OLS) algorithm is popularly used in sparse recovery, subset selection, and function approximation. In this paper, we analyze the performance guarantee of OLS. Specifically, we show that if a sampling matrix Φ has unit ℓ2-norm columns and satisfies the restricted isometry property (RIP) of order K + 1 withthen OLS exactly recovers any K-sparse vector x from its measurements y = Φx in K iterations. Furthermore, we show that the proposed guarantee is optimal in the sense that OLS may fail the recovery under δK+1 ≥ CK . Additionally, we show that if the columns of a sampling matrix are ℓ2-normalized, then the proposed condition is also an optimal recovery guarantee for the orthogonal matching pursuit (OMP) algorithm. Also, we establish a recovery guarantee of OLS in the more general case where a sampling matrix might not have unit ℓ2-norm columns. Moreover, we analyze the performance of OLS in the noisy case. Our result demonstrates that under a suitable constraint on the minimum magnitude of nonzero elements in an input signal, the proposed RIP condition ensures OLS to identify the support exactly. Index Terms-Orthogonal least squares (OLS), orthogonal matching pursuit (OMP), restricted isometry property (RIP), sparse recoveryOn the other hand, it has been reported in [6] that when K = 2, there exists a counterexample for which OLS fails 1 √

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“…where (a) is because P ⊥ T k φ j 2 ≤ φ j 2 = 1 for each of j ∈ Ω \ T . Clearly, the bound in (22) is tighter than that in (21) by the factor of 2 √ 3 . ii) In [6], by putting…”

Section: Lemma 3 ([2 Theorem 1]mentioning

confidence: 97%

A Near-Optimal Condition for Exact Sparse Recovery with Orthogonal Least Squares

Kim

Shim

2019

2019 IEEE/CIC International Conference on Communications in China (ICCC)

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“…where (a) follows from Lemma 2.1 in [19] and (b) holds because N KcM Φ satisfies RIP with constant δ K , and (c) is true since δ 2 ≤ δ K for K ≥ 2. Therefore, µ c = max 1≤i =j≤N | ci,cj | ci 2 cj 2 ≤ δK 1−δK .…”

Section: Appendix a Proof Of Theoremmentioning

confidence: 99%

Fusion-Based Cooperative Support Identification for Compressive Networked Sensing

Yang

Wang

et al. 2020

IEEE Wireless Commun. Lett.

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This paper proposes a fusion-based cooperative support identification scheme for distributed compressive sparse signal recovery via resource-constrained wireless sensor networks. The proposed support identification protocol involves: (i) local sparse sensing for economizing data gathering and storage, (ii) local binary decision making for partial support knowledge inference, (iii) binary information exchange among active nodes, and (iv) binary data aggregation for support estimation. Then, with the aid of the estimated signal support, a refined local decision is made at each node. Only the measurements of those informative nodes will be sent to the fusion center, which employs a weighted ℓ1-minimization for global signal reconstruction. The design of a Bayesian local decision rule is discussed, and the average communication cost is analyzed. Computer simulations are used to illustrate the effectiveness of the proposed scheme.

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“…Its basic theory is using the signals sparse feature to represent it losslessly by small data volume [12]. In 1993, Mallat proposed matching pursuit (MP), which is one of the representative sparse decomposition algorithms [13][14][15].…”

Section: Algorithm Basic Principles and Its Applicationmentioning

confidence: 99%

An Improved Fruit Fly Optimization Algorithm and Its Application in Heat Exchange Fouling Ultrasonic Detection

Xia

Sun

et al. 2018

Mathematical Problems in Engineering

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Inspired by the basic theory of Fruit Fly Optimization Algorithm, in this paper, cat mapping was added to the original algorithm, and the individual distribution and evolution mechanism of fruit fly population were improved in order to increase the search speed and accuracy. The flowchart of the improved algorithm was drawn to show its procedure. Using classical test functions, simulation optimization results show that the improved algorithm has faster and more reliable optimization ability. The algorithm was then combined with sparse decomposition theory and used in processing fouling detection ultrasonic signals to verify the validity and practicability of the improved algorithm.

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

Cited by 32 publications

References 27 publications

A Near-Optimal Condition for Exact Sparse Recovery with Orthogonal Least Squares

A Near-Optimal Condition for Exact Sparse Recovery with Orthogonal Least Squares

Fusion-Based Cooperative Support Identification for Compressive Networked Sensing

An Improved Fruit Fly Optimization Algorithm and Its Application in Heat Exchange Fouling Ultrasonic Detection

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