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Stable Recovery of Sparse Signals and an Oracle Inequality

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3 Author(s)
Tony Tony Cai ; Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA, USA ; Lie Wang ; Guangwu Xu

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.

Published in:

IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 7 )