  Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive
algorithm for sparse recovery. Recent developments have shown that OMP
guarantees exact recovery of K-sparse signals with K or more than K iterations
if the observation matrix satisfies the restricted isometry property (RIP) with
some conditions. We develop RIP-based online guarantees for recovery of a
K-sparse signal with more than K OMP iterations. Though these guarantees cannot
be generalized to all sparse signals a priori, we show that they can still hold
online when the state-of-the-art K-step recovery guarantees fail. In addition,
we present bounds on the number of correct and false indices in the support
estimate for the derived condition to be less restrictive than the K-step
guarantees. Under these bounds, this condition guarantees exact recovery of a
K-sparse signal within 3K/2 iterations, which is much less than the number of
steps required for the state-of-the-art exact recovery guarantees with more
than K steps. Moreover, we present phase transitions of OMP in comparison to
basis pursuit and subspace pursuit, which are obtained after extensive recovery
simulations involving different sparse signal types. Finally, we empirically
analyse the number of false indices in the support estimate, which indicates
that these do not violate the developed upper bound in practice.
