OMP Based Joint Sparsity Pattern Recovery Under Communication Constraints

We address the problem of joint sparsity pattern recovery based on multiple measurement vectors (MMVs) in resource constrained distributed networks. We assume that distributed nodes observe sparse signals that share a common (but unknown) sparsity pattern. Each node is assumed to sample the sparse signals via different sensing matrices in general. In many distributed communication networks, it is often required that joint sparse recovery be performed under inherent resource constraints such as communication bandwidth and transmit/processing power. We propose two approaches to take the communication constraints into account while performing joint sparsity pattern recovery. First, we explore the use of a shared multiple access channel (MAC) in forwarding observation vectors from 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 linear combinations of the observations. We discuss the conditions under which the common sparsity pattern can be recovered reliably. Second, we develop two efficient 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 collaborates with neighboring nodes by sharing a small amount of information at different stages while estimating the indices of the true sparsity pattern in a greedy manner. The tradeoff between the performance gain and the communication overhead of the proposed algorithms is demonstrated via simulations.