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Time-Varying Graph Signal Recovery Based on Low-Rank and Piecewise-Differential Smoothness.

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Title: Time-Varying Graph Signal Recovery Based on Low-Rank and Piecewise-Differential Smoothness.
Authors: Liu, Jinling1,2,3 (AUTHOR) liujl@guet.edu.cn, Wang, Junyi2 (AUTHOR) wangjy@guet.edu.cn, Li, Guozhi1,3 (AUTHOR) liguozhi@guet.edu.cn, Lan, Chaowang1,3 (AUTHOR) chaowanglan@guet.edu.cn, Liu, Zhenbing1,3,4 (AUTHOR) zbliu@guet.edu.cn
Source: Circuits, Systems & Signal Processing. Jul2026, Vol. 45 Issue 7, p5546-5572. 27p.
Subjects: Spatiotemporal processes, Difference operators, Smoothness of functions, Signal processing, Signal reconstruction
Abstract: Time-varying piecewise smooth data recovery problem exists extensively in computer vision, image processing, environment monitoring, etc. In recent years, the emerging field of graph signal processing (GSP) 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 jointly exploiting the graph difference operator and the time difference operator to capture the spatio-temporal correlation of the data, we obtain a method based on low-rank and piecewise-differential smoothness (LRPDS). The proposed method achieves high recovery accuracy by jointly exploiting low rank property, the piece- wise smoothness and differential smoothness of graph signals. Numerical results on three real-world datasets demonstrate that our scheme has better reconstruction performance compared with existing model-based matrix completion approaches. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Time-varying piecewise smooth data recovery problem exists extensively in computer vision, image processing, environment monitoring, etc. In recent years, the emerging field of graph signal processing (GSP) 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 jointly exploiting the graph difference operator and the time difference operator to capture the spatio-temporal correlation of the data, we obtain a method based on low-rank and piecewise-differential smoothness (LRPDS). The proposed method achieves high recovery accuracy by jointly exploiting low rank property, the piece- wise smoothness and differential smoothness of graph signals. Numerical results on three real-world datasets demonstrate that our scheme has better reconstruction performance compared with existing model-based matrix completion approaches. [ABSTRACT FROM AUTHOR]
ISSN:0278081X
DOI:10.1007/s00034-025-03398-x