Stable Recovery of Sparse Signals and an Oracle Inequality
Tony Cai, Lie Wang and Guangwu Xu
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Abstract:
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. Both bounded noise and Gaussian noise
settings are considered. Furthermore, the condition is shown to be sharp.
In addition, an oracle inequality is given under the mutual incoherence
condition.
- Paper:
pdf file.
- Other related papers:
Cai, T., Xu, G. & Zhang, J. (2009).
On recovery of sparse signals via l1 minimization.
IEEE Transactions on Information Theory 55 , 3388-3397.Cai, T., Wang, L. & Xu, G. (2010).
Shifting inequality and recovery of sparse signals.
IEEE Transactions on Signal Processing 58, 1300-1308.