Decentralized and Collaborative Subspace Pursuit: A Communication-Efficient Algorithm for Joint Sparsity Pattern Recovery

In this paper, we consider the problem of joint sparsity pattern recovery in a decentralized network and propose an algorithm named decentralized and collaborative subspace pursuit (DCSP). The basic idea of DCSP is to embed collaboration among nodes into each iteration of the standard subspace pursuit (SP) algorithm. At each iteration of the DCSP algorithm, local estimation of the support set is carried out at every node by finding the subspace that the local measurement vector most probably lies in, and then the global estimate of the support set is obtained by fusion of all the local estimates. An attractive characteristic of DCSP is the small number of messages to be transmitted among nodes, which is helpful when the communication capacity of the network is limited. Compared to existing decentralized greedy algorithms, DCSP offers satisfactory accuracy of sparsity pattern recovery with much less communication cost. We further extend DCSP to the generalized DCSP (GDCSP) algorithm, by allowing each node to share more local information with its surrounding neighbors. GDCSP outperforms DCSP in terms of the accuracy of sparsity pattern recovery at the cost of slightly increased communication overhead.