Generic cooperative and distributed algorithm for recovery of signals with the same sparsity profile in wireless sensor networks: a non-convex approach

Most of the wireless sensor networks (WSNs) are equipped with battery-powered devices with limited processing/communication resources which necessitate the designed algorithms to reduce the computational burden on nodes as much as possible. This could be achieved using distributed algorithms in which the computations are distributed between all of the nodes. In WSNs, the sensors observe phenomena that could be common to some of them, in addition to the intra-signal correlation; therefore, the acquired signals by the sensors possess some inter-signal correlation. These joint structures could be exploited if the designed algorithms are cooperative. On this basis, in this paper a new distributed and cooperative signal recovery algorithm in the application of compressive sensing for WSNs is proposed. We consider a situation that the sensor nodes intend to recover signals that differ from one sensor to another, in the underdetermined systems of equations, while these signals have common sparsity profile. In fact, we introduce a general structure which can be applied to many optimization problems with different non-convex objective functions and different constraints. In this paper, this method will be used on three problems with different constraints and will result in three completely distributed methods. The simulation results show that the proposed method presents better performance compared to the other existing algorithms in terms of both recovery and convergence rate.