Cooperative sparsity pattern recovery in distributed networks via distributed-OMP

In this paper, we address the problem of sparsity pattern recovery of a sparse signal with multiple measurement data in a distributed network. We consider that each node in the network makes measurements via random projections regarding the same sparse signal. We propose a distributed greedy algorithm based on Orthogonal Matching Pursuit (OMP) in which the locations of non zero coefficients of the sparse signal are estimated iteratively while performing fusion of estimates at distributed nodes. In the proposed distributed framework, each node has to perform less number of iterations of OMP compared to the sparsity index of the sparse signal. With each node having a very small number of compressive measurements, a significant performance gain in sparsity pattern detection is achieved via the proposed collaborative scheme compared to the case where each node estimates the sparsity pattern independently and then fusion is performed to get a global estimate. We further extend the algorithm to a binary hypothesis testing framework, where the algorithm first detects the presence of a sparse signal collaborating among nodes with a fewer number of iterations of OMP and then increases the number of iterations to estimate the sparsity pattern only if the signal is detected.