  In this paper, we consider the problem of joint sparsity pattern recovery in
a distributed sensor network. The sparse multiple measurement vector signals
(MMVs) observed by all the nodes are assumed to have a common (but unknown)
sparsity pattern. To accurately recover the common sparsity pattern in a
decentralized manner with a low communication overhead of the network, we
develop an algorithm named decentralized and collaborative subspace pursuit
(DCSP). In DCSP, each node is required to perform three kinds of operations per
iteration: 1) estimate the local sparsity pattern by finding the subspace that
its measurement vector most probably lies in; 2) share its local sparsity
pattern estimate with one-hop neighboring nodes; and 3) update the final
sparsity pattern estimate by majority vote based fusion of all the local
sparsity pattern estimates obtained in its neighborhood. The convergence of
DCSP is proved and its communication overhead is quantitatively analyzed. We
also propose another decentralized algorithm named generalized DCSP (GDCSP) by
allowing more information exchange among neighboring nodes to further improve
the accuracy of sparsity pattern recovery at the cost of increased
communication overhead. Experimental results show that, 1) compared with
existing decentralized algorithms, DCSP provides much better accuracy of
sparsity pattern recovery at a comparable communication cost; and 2) the
accuracy of GDCSP is very close to that of centralized processing.
