A Distributed 1-bit Compressed Sensing Algorithm Robust to Impulsive Noise

This letter proposes a sparse diffusion algorithm for 1-bit compressed sensing (CS) in wireless sensor networks, and the algorithm is inherently robust against impulsive noise. The approach exploits the diffusion strategy from distributed learning in the 1-bit CS framework. To estimate a common sparse vector cooperatively from only the sign of measurements, a steepest descent method that minimizes the suitable global and local convex cost functions is used. A diffusion strategy is suggested for distributive learning of the sparse vector. A new application of the proposed algorithm to sparse channel estimation is also introduced. The proposed sparse diffusion algorithm is compared with both the state-of-the-art nondistributed and distributed algorithms. Simulation results show the effectiveness of the proposed distributed algorithm and its robustness against impulsive noise. Furthermore, the sparse channel estimation results show the superior performance of the proposed algorithm to other algorithms under impulsive noise environment.