Graph-based Reconstruction of Time-varying Spatial Signals

Signal processing on graphs is an emerging field studying signals in irregular domains, and has been applied to many applications such as sensor networks and recommendation systems. In this paper, a novel method for the recovery of time-varying spatial signal based on graph is proposed. A graph is established according to the spatial position of the signal. Unlike the previous works, the smoothness of the temporal differential signal on the graph rather than the smoothness of the signal itself is used to help reconstruction. Two experiments of real-world are conducted. The first experiment of sea surface temperature data shows that the proposed algorithm achieves less reconstruction error than other algorithms, and the second experiment of sensor network data demonstrates the rationality and superiority of the proposed algorithms from intuition.