Distributed Multi-View Sparse Vector Recovery

Abstract

In this paper, we consider a multi-view compressed sensing problem, where each sensor can only obtain a partial view of the global sparse vector. Here the partial view means that some arbitrary and unknown indices of the global vector are unobservable to that sensor and do not contribute to the measurement outputs. The sensors aim to collaboratively recover the global state vector in a decentralized manner. We formulate this recovery problem as a bilinear optimization problem relying on a factored joint sparsity model (FJSM), in which the variables are factorized into a node-specific sparse local masking vector and the desired common sparse global vector. We first theoretically analyze the general conditions guaranteeing the global vector's successful recovery. Then we propose a novel in-network algorithm based on the powerful distributed alternating direction method of multipliers (ADMM), which can reconstruct the vectors and achieve consensus among nodes concerning the estimation of the global vector. Specifically, each node alternately updates the common global vector and its local masking vector, and then it transfers the estimated global vector to its neighboring nodes for further updates. To avoid potential divergence of the iterative algorithm, we propose an early stopping rule for the estimation of the local masking vectors and further conceive an estimation error-mitigation algorithm. The convergence of the proposed algorithms is theoretically proved. Finally, extensive simulations validate their excellent performance both in terms of the convergence and recovery accuracy.