  A sufficient condition reported very recently for perfect recovery of a
K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that
the restricted isometry constant of the sensing matrix satisfies
delta_K+1<1/(sqrt(delta_K+1)+1). By exploiting an approximate orthogonality
condition characterized via the achievable angles between two orthogonal sparse
vectors upon compression, this paper shows that the upper bound on delta can be
further relaxed to delta_K+1<(sqrt(1+4*delta_K+1)-1)/(2K).This result thus
narrows the gap between the so far best known bound and the ultimate
performance guarantee delta_K+1<1/(sqrt(delta_K+1)) that is conjectured by Dai
and Milenkovic in 2009. The proposed approximate orthogonality condition is
also exploited to derive less restricted sufficient conditions for signal
reconstruction in several compressive sensing problems, including signal
recovery via OMP in a noisy environment, compressive domain interference
cancellation, and support identification via the subspace pursuit algorithm.
