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This paper considers signal recovery through an unconstrained minimization inthe framework of mutual incoherence property. A sufficient condition isprovided to guarantee the stable recovery in the noisy case. And we give alower bound for the $\ell_2$ norm of difference of reconstructed signals andthe original signal, in the sense of expectation and probability. Furthermore,oracle inequalities of both sparse signals and non-sparse signals are derivedunder the mutual incoherence condition in the case of Gaussian noises. Finally,we investigate the relationship between mutual incoherence property and robustnull space property and find that robust null space property can be deducedfrom the mutual incoherence property.

Signal Recovery under Mutual Incoherence Property and Oracle Inequalities