Results 11 to 20 of about 794 (157)
The Road to Deterministic Matrices with the Restricted Isometry Property [PDF]
Journal of Fourier Analysis and Applications, 2013 The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success.
Bandeira, Afonso S. +3 more
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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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The Restricted Isometry Property of Subsampled Fourier Matrices [PDF]
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, 2015 A matrix $A \in \mathbb{C}^{q \times N}$ satisfies the restricted isometry property of order $k$ with constant $\varepsilon$ if it preserves the $\ell_2$ norm of all $k$-sparse vectors up to a factor of $1\pm \varepsilon$. We prove that a matrix $A$ obtained by randomly sampling $q = O(k \cdot \log^2 k \cdot \log N)$ rows from an $N \times N$ Fourier ...
Ishay Haviv, Oded Regev 0001
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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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Perturbations of Compressed Data Separation With Redundant Tight Frames
IEEE Access, 2018 In the era of big data, the multi-modal data can be seen everywhere. Research on such data has attracted extensive attention in the past few years. In this paper, we investigate the perturbations of compressed data separation with redundant tight frames ...
Feng Zhang +4 more
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Orthogonal Matching Pursuit Under the Restricted Isometry Property [PDF]
Constructive Approximation, 2016 12 ...
Albert Cohen +2 more
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The Average-Case Time Complexity of Certifying the Restricted Isometry Property [PDF]
IEEE Transactions on Information Theory, 2021 In compressed sensing, the restricted isometry property (RIP) on $M \times N$ sensing matrices (where $M < N$) guarantees efficient reconstruction of sparse vectors. A matrix has the $(s,δ)$-$\mathsf{RIP}$ property if behaves as a $δ$-approximate isometry on $s$-sparse vectors. It is well known that an $M\times N$ matrix with i.i.d. $\mathcal{N}(0,1/
Yunzi Ding +3 more
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