Tracking Time-Vertex Propagation using Dynamic Graph Wavelets
This work addresses the analysis of dynamic graph signals, which is crucial for applications like seismology, but it appears incremental as it extends existing wavelet and compressive sensing techniques to time-vertex domains.
The authors tackled the problem of analyzing time-evolving graph signals, such as wave propagation on networks, by proposing Dynamic Graph Wavelets, a novel class of wavelet frames that incorporate both time and graph dimensions. They demonstrated the method's efficiency on real seismological data, enabling estimation of earthquake epicenters from seismic network recordings.
Graph Signal Processing generalizes classical signal processing to signal or data indexed by the vertices of a weighted graph. So far, the research efforts have been focused on static graph signals. However numerous applications involve graph signals evolving in time, such as spreading or propagation of waves on a network. The analysis of this type of data requires a new set of methods that fully takes into account the time and graph dimensions. We propose a novel class of wavelet frames named Dynamic Graph Wavelets, whose time-vertex evolution follows a dynamic process. We demonstrate that this set of functions can be combined with sparsity based approaches such as compressive sensing to reveal information on the dynamic processes occurring on a graph. Experiments on real seismological data show the efficiency of the technique, allowing to estimate the epicenter of earthquake events recorded by a seismic network.