The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit
The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit
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DOI：
10.1109/lsp.2012.2233734
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发表时间：
2013-04
影响因子：
3.9
通讯作者：
Rui Wu;Wei Huang;Dirong Chen
中科院分区：
文献类型：
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作者：
Rui Wu;Wei Huang;Dirong Chen
正交匹配追踪（OMP）算法是压缩感知中一种经典的贪婪算法.在这封信中，我们研究了OMP的性能恢复稀疏信号的支持，从一些嘈杂的线性测量。我们考虑两种类型的有界噪声和我们的分析是在限制等距属性（RIP）的框架。结果表明，在RIP和稀疏信号的非零元素的最小幅度的一定条件下，OMP与适当的停止规则可以恢复支持的信号从噪声的观察。我们还讨论了高斯噪声的情况。我们的条件RIP改进了一些现有的结果。
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.