arXiv subjects

Gal Morgenstern

Publications and source records attributed to Gal Morgenstern.

3 recordsLinked to original sources

arXiv2024

Efficient Recovery of Sparse Graph Signals from Graph Filter Outputs

This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the field of graph signal processing (GSP). Sparse graph signals can be used in the modeling of a variety of real-world applications in networks, such as social, biological, and power systems, and enable various GSP tasks, such as graph signal reconstruction, blind deconvolution, and sampling. In this paper, we assume double sparsity of both the graph signal and the graph topology, as well as a low-order graph filter. We propose three algorithms to reconstruct the support set of the input sparse graph signal from the graph filter output samples, leveraging these assumptions and the generalized information criterion (GIC). First, we describe the graph multiple GIC (GM-GIC) method, which is based on partitioning the dictionary elements (graph filter matrix columns) that capture information on the signal into smaller subsets. Then, the local GICs are computed for each subset and aggregated to make a global decision. Second, inspired by the well-known branch and bound (BNB) approach, we develop the graph-based branch and bound GIC (graph-BNB-GIC), and incorporate a new tractable heuristic bound tailored to the graph and graph filter characteristics. In addition, we propose the graph-based first order correction (GFOC) method, which improves existing sparse recovery methods by iteratively examining potential improvements to the GIC cost function by replacing elements from the estimated support set with elements from their one-hop neighborhood. In addition, we investigate the application of our graph-based sparse recovery methods in blind deconvolution scenarios where the graph filter is unknown.

eess.SP↗

arXiv2023

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. Recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification using the representation of the power system voltages as smooth graph signals. Within this framework, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. We present the GFDI attack as the solution for a non-convex constrained optimization problem. The solution to the GFDI attack problem is obtained through approximating it using $\ell_1$ relaxation. A series of quadratic programming problems that are classified as convex optimization problems are solved to obtain the final solution. We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to a high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 and IEEE-118 bus test cases reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

eess.SP↗

arXiv2022

Structural-constrained Methods for the Identification of Unobservable False Data Injection Attacks in Power Systems

Power system functionality is determined on the basis of the power system state estimation (PSSE). Thus, corruption of the PSSE may lead to severe consequences, such as financial losses, maintenance damage, and disruptions in electricity distribution. Classical bad data detection (BDD) methods, developed to ensure PSSE reliability, are unable to detect well-designed attacks, named unobservable false data injection (FDI) attacks. In this paper, we develop novel structural-constrained methods for the detection of unobservable FDI attacks, the identification of the attacked buses' locations, and PSSE under the presence of such attacks. The proposed methods are based on formulating structural, sparse constraints on both the attack and the system loads. First, we exploit these constraints in order to compose an appropriate model selection problem. Then, we develop the associated generalized information criterion (GIC) for this problem. However, for large networks, the GIC method's computational complexity grows exponentially with the network size. Thus, based on the proposed structural and sparse constraints, we develop two novel low-complexity methods for unobservable FDI attack identification: 1) a modification of the state-of-the-art orthogonal matching pursuit (OMP); and 2) a method that utilizes the graph Markovian property in power systems, i.e. the second-neighbor relationship between the power data at the system's buses. The methods' performance is evaluated on a IEEE-30 bus test case system.

eess.SP↗