Secure Blind Graph Signal Recovery and Adversary Detection Using Smoothness Maximization

Abstract: In this letter, we propose a secure blind Graph Signal Recovery (GSR) algorithm that can detect adversary nodes. Some unknown adversaries are assumed to be injecting false data at their respective nodes in the graph. The number and location of adversaries are not known in advance and the goal is to recover the graph signal in the presence of measurement noise and False Data Injection (FDI) caused by the adversaries. Consequently, the proposed algorithm would be a perfect candidate to solve this challenging problem. Moreover, due to the presence of malicious nodes, the proposed method serves as a secure GSR algorithm. For adversary detection, a statistical measure based on differential smoothness is used. Specifically, the difference between the current observed smoothness and the average smoothness excluding the corresponding node. This genuine statistical approach leads to an effective and low-complexity adversary detector. In addition, following malicious node detection, the GSR is performed using a variant of smoothness maximization, which is solved efficiently as a fractional optimization problem using a Dinkelbach's algorithm. Analysis of the detector, which determines the optimum threshold of the detector is also presented. Simulation results show a significant improvement of the proposed method in signal recovery compared to the median GSR algorithm and other competing methods.