  The most frequently used condition for sampling matrices employed in
compressive sampling is the restricted isometry (RIP) property of the matrix
when restricted to sparse signals. At the same time, imposing this condition
makes it difficult to find explicit matrices that support recovery of signals
from sketches of the optimal (smallest possible)dimension. A number of attempts
have been made to relax or replace the RIP property in sparse recovery
algorithms. We focus on the relaxation under which the near-isometry property
holds for most rather than for all submatrices of the sampling matrix, known as
statistical RIP or StRIP condition. We show that sampling matrices of
dimensions $m\times N$ with maximum coherence $\mu=O((k\log^3 N)^{-1/4})$ and
mean square coherence $\bar \mu^2=O(1/(k\log N))$ support stable recovery of
$k$-sparse signals using Basis Pursuit. These assumptions are satisfied in many
examples. As a result, we are able to construct sampling matrices that support
recovery with low error for sparsity $k$ higher than $\sqrt m,$ which exceeds
the range of parameters of the known classes of RIP matrices.
