  We study statistical restricted isometry, a property closely related to
sparse signal recovery, of deterministic sensing matrices of size $m \times N$.
A matrix is said to have a statistical restricted isometry property (StRIP) of
order $k$ if most submatrices with $k$ columns define a near-isometric map of
${\mathbb R}^k$ into ${\mathbb R}^m$. As our main result, we establish
sufficient conditions for the StRIP property of a matrix in terms of the mutual
coherence and mean square coherence. We show that for many existing
deterministic families of sampling matrices, $m=O(k)$ rows suffice for
$k$-StRIP, which is an improvement over the known estimates of either $m =
\Theta(k \log N)$ or $m = \Theta(k\log k)$. We also give examples of matrix
families that are shown to have the StRIP property using our sufficient
conditions.
