Thresholding based Stochastic Robust Algorithm for Distributed Compressed Sensing

In this paper, we first present a stochastic gradient based robust algorithm for recovering a sparse signal from compressed measurements corrupted by impulsive noise for large problems where calculation of the full gradient is expensive. This stochastic gradient based strategy is then modified and applied to diffusion based distributed compressed sensing. In the proposed algorithm, a proxy to the actual gradient is found and hard thresholding based updates are carried out. The proposed algorithm uses Lorentzian norm of the residual as the cost function, making it robust against impulsive noise. It is observed through simulations that the proposed algorithm is able to outperform existing stochastic gradient based algorithms and is able to provide at par recovery performance to that of other robust deterministic algorithms currently available in literature for distributed compressed sensing.