Time-varying signal recovery based on low rank and graph-time smoothness

• Published in: Digital signal processing 2023-03, Vol.133, p.103821, Article 103821
• Main Authors: Liu, Jinling, Lin, Jiming, Qiu, Hongbing, Wang, Junyi, Nong, Liping
• Format: Article
• Language: English
• Subjects: Graph signal processing; Hodrick-Prescott filter; Matrix completion; Time-varying signal recovery
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1016/j.dsp.2022.103821

Time-varying data recovery problem exists extensively in computer vision, image processing, environment monitoring, etc. In recent years, the emerging field of graph signal processing provides a new way to solve this problem, deriving the graph signal matrix completion (GSMC) which incorporates the correlation among data entries. The model-based methods of GSMC are more interpretable, but their reconstruction quality is still not satisfactory, especially when observations are sparse. In this paper, we propose a new matrix completion method to solve the time-varying data recovery problem. By adopting the time series analysis method to capture the evolution of data in the time dimension, we obtain a method based on Low Rank and Graph-Time Smoothness (LRGTS). The proposed method has high recovery accuracy by using the second-order information associated with the problem. Numerical results on three real-world datasets demonstrate that our scheme has better reconstruction performance when known entries are sparse, compared with existing matrix completion approaches. •A graph signal matrix completion method utilizing the second-order smoothness is proposed.•The method shows superior recovery performance.•Simulation results on real-world datasets verify the effectiveness of the method.