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Decay Properties of Restricted Isometry Constants [PDF]
IEEE Signal Processing Letters, 2009 Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix's restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds; however, members of many random matrix ensembles typically satisfy
Jeffrey D. Blanchard +2 more
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Applied Sciences, 2023 Currently, the use of microseismic detection technology for crack detection and localization in rock masses has great potential in detecting structural damage.
Jinfeng Chen, Meng Mei
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A Method of Reweighting the Sensing Matrix for Compressed Sensing
IEEE Access, 2021 In compressed sensing, a small enough restricted isometry constant (RIC) of the sensing matrix satisfying the restricted isometry property (RIP) is the powerful guarantee on the precise reconstruction of a sparse discrete signal.
Lei Shi, Gangrong Qu, Qian Wang
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Suprema of Chaos Processes and the Restricted Isometry Property [PDF]
Communications on Pure and Applied Mathematics, 2014 We present a new bound for suprema of a special type of chaos process indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time‐frequency structured random matrices.
Krahmer, Felix +2 more
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An Armijo-Type Hard Thresholding Algorithm for Joint Sparse Recovery
IEEE Access, 2021 Joint sparse recovery (JSR) in compressed sensing simultaneously recovers sparse signals with a common sparsity structure from their multiple measurement vectors obtained through a common sensing matrix.
Lili Pan, Xunzhi Zhu
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Efficiency of orthogonal super greedy algorithm under the restricted isometry property
Journal of Inequalities and Applications, 2019 We investigate the efficiency of orthogonal super greedy algorithm (OSGA) for sparse recovery and approximation under the restricted isometry property (RIP).
Xiujie Wei, Peixin Ye
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A new bound on the block restricted isometry constant in compressed sensing
Journal of Inequalities and Applications, 2017 This paper focuses on the sufficient condition of block sparse recovery with the l 2 / l 1 $l_{2}/l_{1}$ -minimization. We show that if the measurement matrix satisfies the block restricted isometry property with δ 2 s | I < 0.6246 $\delta_{2s|\mathcal{I}
Yi Gao, Mingde Ma
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IEEE Access, 2018 Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering the support of a sparse signal x from the underdetermined model y = Ax. In practice, we should analyze the performance of OMP under general perturbations, which means that
Haifeng Li, Guoqi Liu
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Survey on compressed sensing over the past two decades
Memories - Materials, Devices, Circuits and Systems, 2023 Compressed Sensing (CS) is a novel data acquisition theorem exploiting the signals sparsity differing from traditional Nyquist theorem in the ability of obtaining all information of such signal in fewer samples.
Sherif Hosny +2 more
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Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements
Journal of Applied Mathematics, 2013 The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images.
Qingshan You, Qun Wan, Haiwen Xu
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