A Distributed Algorithm for Reconstructing Time-Varying Graph Signals

• Published in: Circuits, systems, and signal processing Vol. 41; no. 6; pp. 3624 - 3641
• Main Authors: Chi, Yuan, Jiang, Junzheng, Zhou, Fang, Xu, Shuwen
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Algorithms; Approximation; Circuits and Systems; Computer networks; Convergence; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Newton methods; Optimization; Reconstruction; Regularization; Short Paper; Signal processing; Signal,Image and Speech Processing; Smoothness; Time-varying graph signal reconstruction; Matrix inverse approximation; Distributed algorithm
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-021-01930-3

The reconstruction of time-varying signals on graphs is a prominent problem in graph signal processing community. By imposing the smoothness regularization over the time-vertex domain, the reconstruction problem can be formulated into an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and regularization term. In this paper, we propose an approximate Newton method to solve the problem in a distributed manner, which is applicable for spatially distributed systems consisting of agents with limited computation and communication capacity. The algorithm has low computational complexity while nearly maintains the fast convergence of the second-order methods, which is evidently better than the existing reconstruction algorithm based on the gradient descent method. The convergence of the proposed algorithm is explicitly proved. Numerical results verify the validity and fast convergence of the proposed algorithm.