  We consider the problem of recovering fusion frame sparse signals from
incomplete measurements. These signals are composed of a small number of
nonzero blocks taken from a family of subspaces. First, we show that, by using
a-priori knowledge of a coherence parameter associated with the angles between
the subspaces, one can uniformly recover fusion frame sparse signals with a
significantly reduced number of vector-valued (sub-)Gaussian measurements via
mixed l^1/l^2-minimization. We prove this by establishing an appropriate
version of the restricted isometry property. Our result complements previous
nonuniform recovery results in this context, and provides stronger stability
guarantees for noisy measurements and approximately sparse signals. Second, we
determine the minimal number of scalar-valued measurements needed to uniformly
recover all fusion frame sparse signals via mixed l^1/l^2-minimization. This
bound is achieved by scalar-valued subgaussian measurements. In particular, our
result shows that the number of scalar-valued subgaussian measurements cannot
be further reduced using knowledge of the coherence parameter. As a special
case it implies that the best known uniform recovery result for block sparse
signals using subgaussian measurements is optimal.
