Federated Consensus-Based Algorithm for Stable Recovery of Sparse Signals

In this article, we develop a new algorithm, named federated consensus-based algorithm (FCB), for sparse recovery, and show its performance in terms of both support recovery and signal recovery. Specifically, FCB is designed on the basis of the federated computational architecture, to increase the computational parallelism and accelerate the convergence. The algorithm design is realized by integrating accelerated projection-based consensus (APC) with greedy techniques. Then, the conditions of exact support recovery and an upper bound of signal recovery error are derived for FCB in the noisy case. From the explicit expression of the signal recovery error bound, it is confirmed that FCB can stably recover sparse signals under appropriate conditions using the coherence statistic of the measurement matrix and the minimum magnitude of nonzero elements of the signal. Experimental results illustrate the performance of FCB, validating our derived conditions of exact support recovery and upper bound of signal recovery error. In summary, FCB utilizes the federated computational architecture, enabling high parallelism and fast convergence, and uses greedy techniques to guarantee stable recovery performance.