  In compressive sensing, a small collection of linear projections of a sparse
signal contains enough information to permit signal recovery. Distributed
compressive sensing (DCS) extends this framework by defining ensemble sparsity
models, allowing a correlated ensemble of sparse signals to be jointly
recovered from a collection of separately acquired compressive measurements. In
this paper, we introduce a framework for modeling sparse signal ensembles that
quantifies the intra- and inter-signal dependencies within and among the
signals. This framework is based on a novel bipartite graph representation that
links the sparse signal coefficients with the measurements obtained for each
signal. Using our framework, we provide fundamental bounds on the number of
noiseless measurements that each sensor must collect to ensure that the signals
are jointly recoverable.
