Greedy Block Coordinate Descent under Restricted Isometry Property

Wen, Jinming; Tang, Jie; Zhu, Fayan

doi:10.1007/s11036-016-0774-9

Cited by 6 publications

(9 citation statements)

References 17 publications

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“…This work focuses on the single measurement vector problem. Other works focused on Multiple Measurement Vectors (MMV) can be found in [26]- [29]. Some open research challenges related to sparse signal estimation are also discussed.…”

Section: Introductionmentioning

confidence: 99%

A Review of Sparse Recovery Algorithms

et al. 2019

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Nowadays, a large amount of information has to be transmitted or processed. This implies highpower processing, large memory density, and increased energy consumption. In several applications, such as imaging, radar, speech recognition, and data acquisition, the signals involved can be considered sparse or compressive in some domain. The compressive sensing theory could be a proper candidate to deal with these constraints. It can be used to recover sparse or compressive signals with fewer measurements than the traditional methods. Two problems must be addressed by compressive sensing theory: design of the measurement matrix and development of an efficient sparse recovery algorithm. These algorithms are usually classified into three categories: convex relaxation, non-convex optimization techniques, and greedy algorithms. This paper intends to supply a comprehensive study and a state-of-the-art review of these algorithms to researchers who wish to develop and use them. Moreover, a wide range of compressive sensing theory applications is summarized and some open research challenges are presented.

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Section: Introductionmentioning

confidence: 99%

A Review of Sparse Recovery Algorithms

et al. 2019

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“…In many application domains, such as multivariate regression [1], face recognition [2], direction of arrival estimation of multiple narrowband signals [3], [4], we need to reconstruct sparse matrix X ∈ R N ×P from the model…”

Section: Introductionmentioning

confidence: 99%

“…and (b) is from(4) with B = P ⊥ [ ] [ \ ] and D = X [ \ ]. Thus, (5) holds.The following lemma provides an upper bound on the BMMV decision-metric for the columns belonging to c .Lemma Let in (1) obey the K + 1 order block RIP with…”

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confidence: 99%

Sparse Recovery With Block Multiple Measurement Vectors Algorithm

2019

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This paper investigates the performance of the block multiple measurement vectors (BMMV) algorithm in reconstructing block joint sparse matrices. We prove that if obeys block restricted isometry property with δ K +1 < 1 √ K +1 , then BMMV perfectly reconstructs any block K-joint sparse matrix X from observations Y = X in K iterations. We also show that BMMV may not reconstruct block K-joint sparse matrices in K iterations under the condition δ K +1 ≥ 1 √ K +1. That is to say, the condition δ K +1 < 1 √ K +1 is optimal for the BMMV algorithm. INDEX TERMS Sparse recovery, block restricted isometry property, block multiple measurement vectors (BMMV) algorithm.

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“…Remark In Theorem 3.1, if