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Low-rank Updates in Slowly Time-varying Graphs for Spatial-Temporal Signal Interpolation

arXiv 2606.24011 ↗First posted 22 Jun 2026eess.SP cs.LGcited by 0

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Abstract (arXiv)

A crucial assumption in graph signal processing (GSP) is the existence of an underlying graph that captures the pairwise similarities between nodes, allowing filters to be designed based on this graph for tasks such as denoising. For spatial-temporal data in which node-to-node similarities evolve over time, a static spatial graph is insufficient. In this paper, to represent slowly time-varying pairwise relationships, we model the graph changes in two consecutive adjacency matrices P = W(2) - W(1) across time as a low-rank matrix. % Specifically, given an initial adjacency matrix W(1) at time t=1, we jointly interpolate a signal x2 and estimate W(2) at t=2 using both a graph signal smoothness prior for x2 and a low-rank prior on P. We alternate optimization steps. With W(2) fixed, x2 is interpolated by solving a linear system. Alternatively, holding x2 fixed, W(2) is updated via proximal gradient descent (PGD). The proximal mapping of the rank term Gamma(W(2) - W(1)) is approximated in linear time using a fast orthogonal matching pursuit (OMP) algorithm that selects a sparse combination of atoms from a dictionary cR formed by the outer products of W(1)'s eigenvectors. We unroll iterations of our algorithm into layers to build a lightweight neural network for limited data-driven parameter tuning. Experiments show that our joint optimization achieves better signal interpolation compared to existing time-varying graph models.

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References · 25

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13 more
  1. 2020Lifelong Graph Learningcited by 31
  2. 2018Graph-Based Blind Image Deblurring From a Single Photographcited by 24
  3. 2020Signed Graph Metric Learning via Gershgorin Disc Perfect Alignmentcited by 15
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