Journal ArticleDOI
The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit
Rui Wu,Wei Huang,Di-Rong Chen +2 more
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TLDR
It is shown that under some conditions on RIP and the minimum magnitude of the nonzero elements of the sparse signal, OMP with proper stopping rules can recover the support of the signal exactly from the noisy observation.Abstract:
Orthogonal matching pursuit (OMP) algorithm is a classical greedy algorithm in Compressed Sensing. In this letter, we study the performance of OMP in recovering the support of a sparse signal from a few noisy linear measurements. We consider two types of bounded noise and our analysis is in the framework of restricted isometry property (RIP). It is shown that under some conditions on RIP and the minimum magnitude of the nonzero elements of the sparse signal, OMP with proper stopping rules can recover the support of the signal exactly from the noisy observation. We also discuss the case of Gaussian noise. Our conditions on RIP improve some existing results.read more
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Journal ArticleDOI
A Sharp Condition for Exact Support Recovery With Orthogonal Matching Pursuit
TL;DR: In this article, the authors show that for any k-sparse signal, if a sensing matrix satisfies the restricted isometry property (RIP) with restricted k+1 constant, then under some constraints on the minimum magnitude of nonzero elements of the signal, OMP can exactly recover the support of k −sparse signals from noisy measurements with OMP in $K$ iterations.
Journal ArticleDOI
An Improved RIP-Based Performance Guarantee for Sparse Signal Recovery via Orthogonal Matching Pursuit
Ling-Hua Chang,Jwo-Yuh Wu +1 more
TL;DR: This paper shows that, in the presence of noise, a relaxed RIC upper bound together with a relaxed requirement on the minimal signal entry magnitude suffices to achieve perfect support identification using OMP.
Journal ArticleDOI
Support Recovery With Orthogonal Matching Pursuit in the Presence of Noise
TL;DR: This article studies the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise and shows that recovery with an arbitrarily small but constant fraction of errors is possible with the OMP algorithm.
Journal ArticleDOI
Compressed Sensing-Aided Downlink Channel Training for FDD Massive MIMO Systems
TL;DR: A compressed sensing-aided channel estimation scheme is proposed, which exploits the observation that the channel statistics change slowly in time, and can estimate the channel with a reduced pilot overhead even when conventional CS cannot be applied.
Proceedings ArticleDOI
Two-stage compressed sensing for millimeter wave channel estimation
Yonghee Han,Jungwoo Lee +1 more
TL;DR: This paper proposes a two-stage CS scheme that requires one-time feedback and is robust to noise, which can be regarded as a compromise between the two approaches.
References
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
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Decoding by linear programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
Posted Content
Decoding by Linear Programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In this paper, it was shown that under suitable conditions on the coding matrix, the input vector can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program).
Proceedings ArticleDOI
Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition
TL;DR: A modification to the matching pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual at every step and thereby leads to improved convergence is proposed.
Journal ArticleDOI
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.
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