  The orthogonal matching pursuit (OMP) algorithm is a commonly used algorithm
for recovering $K$-sparse signals $\x\in \mathbb{R}^{n}$ from linear model
$\y=\A\x$, where $\A\in \mathbb{R}^{m\times n}$ is a sensing matrix. A
fundamental question in the performance analysis of OMP is the characterization
of the probability that it can exactly recover $\x$ for random matrix $\A$.
Although in many practical applications, in addition to the sparsity, $\x$
usually also has some additional property (for example, the nonzero entries of
$\x$ independently and identically follow the Gaussian distribution), none of
existing analysis uses these properties to answer the above question. In this
paper, we first show that the prior distribution information of $\x$ can be
used to provide an upper bound on $\|\x\|_1^2/\|\x\|_2^2$, and then explore the
bound to develop a better lower bound on the probability of exact recovery with
OMP in $K$ iterations. Simulation tests are presented to illustrate the
superiority of the new bound.
