  We address the problem of joint sparsity pattern recovery based on low
dimensional multiple measurement vectors (MMVs) in resource constrained
distributed networks. We assume that distributed nodes observe sparse signals
which share the same sparsity pattern and each node obtains measurements via a
low dimensional linear operator. When the measurements are collected at
distributed nodes in a communication network, it is often required that joint
sparse recovery be performed under inherent resource constraints such as
communication bandwidth and transmit/processing power.
  We present two approaches to take the communication constraints into account
while performing common sparsity pattern recovery. First, we explore the use of
a shared multiple access channel (MAC) in forwarding observations residing at
each node to a fusion center. With MAC, while the bandwidth requirement does
not depend on the number of nodes, the fusion center has access to only a
linear combination of the observations. We discuss the conditions under which
the common sparsity pattern can be estimated reliably. Second, we develop two
collaborative algorithms based on Orthogonal Matching Pursuit (OMP), to jointly
estimate the common sparsity pattern in a decentralized manner with a low
communication overhead. In the proposed algorithms, each node exploits
collaboration among neighboring nodes by sharing a small amount of information
for fusion at different stages in estimating the indices of the true support in
a greedy manner. Efficiency and effectiveness of the proposed algorithms are
demonstrated via simulations along with a comparison with the most related
existing algorithms considering the trade-off between the performance gain and
the communication overhead.
