  We consider compressed sensing of block-sparse signals, i.e., sparse signals
that have nonzero coefficients occurring in clusters. An uncertainty relation
for block-sparse signals is derived, based on a block-coherence measure, which
we introduce. We then show that a block-version of the orthogonal matching
pursuit algorithm recovers block $k$-sparse signals in no more than $k$ steps
if the block-coherence is sufficiently small. The same condition on
block-coherence is shown to guarantee successful recovery through a mixed
$\ell_2/\ell_1$-optimization approach. This complements previous recovery
results for the block-sparse case which relied on small block-restricted
isometry constants. The significance of the results presented in this paper
lies in the fact that making explicit use of block-sparsity can provably yield
better reconstruction properties than treating the signal as being sparse in
the conventional sense, thereby ignoring the additional structure in the
problem.
