Stable Recovery of Sparse Signals and an Oracle Inequality
Stable Recovery of Sparse Signals and an Oracle Inequality
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DOI：
10.1109/tit.2010.2048506
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发表时间：
2010-07-01
影响因子：
2.5
通讯作者：
Xu, Guangwu
中科院分区：
文献类型：
--
作者：
Cai, Tony Tony;Wang, Lie;Xu, Guangwu
本文考虑存在噪声的情况下的稀疏信号恢复。先前用于无噪声情况下精确恢复的互不相干条件被证明足以在有噪声情况下实现稳定恢复。此外，该条件被证明是尖锐的。给出了具体的反例。此外，在高斯噪声的情况下，在互不相干的条件下，推导了预言不等式。
This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise.