  Orthogonal matching pursuit (OMP) is a canonical greedy algorithm for sparse
signal reconstruction. When the signal of interest is block sparse, i.e., it
has nonzero coefficients occurring in clusters, the block version of OMP
algorithm (i.e., Block OMP) outperforms the conventional OMP. In this paper, we
demonstrate that a new notion of block restricted isometry property (Block
RIP), which is less stringent than standard restricted isometry property (RIP),
can be used for a very straightforward analysis of Block OMP. It is
demonstrated that Block OMP can exactly recover any block K-sparse signal in no
more than K steps if the Block RIP of order K+1 with a sufficiently small
isometry constant is satisfied. Using this result it can be proved that Block
OMP can yield better reconstruction properties than the conventional OMP when
the signal is block sparse.
