Decentralized iterative reweighted algorithm for recovery of jointly sparse signals

In a decentralized network where multiple agents exist, each agent takes linearly measurements from the received signal and decodes the corresponding signal by running recovery algorithm at local and also sharing the auxiliary information broadcasted from its neighbors. Motivated by the applications like wireless sensor networks, cooperative spectrum sensing and decentralized event detection in wireless networks, sparse signal recovery or detection in decentralized (distributed) networks has been one of the research focus in wireless network. By exploiting compressive sensing technology, this problem was widely studied in recent years. Although many works have focused on this issue, most of them only consider the situation that all agent (node) measure same signals, like e.g., D-Lasso, DCD-Lasso, which is less suitable for the real wireless network application environment. Thus, this paper proposed a DIRLq (Decentralized Iteratively Reweighted ℓq) algorithm to solve this problem. Different from previous decentralized sparse recovery algorithms like D-Lasso and DCD-Lasso, our algorithm focuses on recovering different signals with joint sparsity structure which were measured in different agents. Besides, although recently proposed DRL1 and DRL2 algorithm have also considered the similar application background, our algorithm presents better performance compared to both of them. Furthermore, we also discuss the convergence behavior of our algorithm. Finally, numerical results are provided to show the effectiveness of our proposed algorithm.