Incremental and diffusion compressive sensing strategies over distributed networks.

Compressive sensing (CS) has been widely used in wireless sensor networks (WSNs). In WSNs, the sensors are battery-powered and hence their communication and processing powers are limited. One of the dominant features of the CS is its complex recovery phase. Thus, great care should be taken into account when designing the CS recovery algorithm for WSNs. In this paper, we propose a distributed and cooperative recovery algorithm for two different cooperation modes of sensor networks including incremental and diffusion. The theoretical performance analysis of the proposed algorithms in both exact and noisy measurements is investigated. The obtained results show the superiority of the proposed method in terms of convergence rate and steady-state error compared with the non-cooperative scenario and the well-known distributed least absolute shrinkage and selection operator (D-LASSO) approach. Furthermore, the proposed structure requires much fewer measurements for exact recovery.