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