Benjamin Girault

Localization bounds for the graph translation

The graph translation operator has been defined with good spectral properties in mind, and in particular with the end goal of being an isometric operator. Unfortunately, the resulting definitions do not provide good intuitions on a vertex-domain interpretation. In this paper, we show that this operator does have a vertex-domain interpretation as a diffusion operator using a polynomial approximation. We show that its impulse response exhibit an exponential decay of the energy way from the impulse, demonstrating localization preservation. Additionally, we formalize several techniques that can be used to study other graph signal operators.

Grasp: A matlab toolbox for graph signal processing

The GraSP toolbox aims at processing and visualizing graphs and graphs signal with ease. In the demo, we show those capabilities using several examples from the literature and from our own experiments.

Towards a definition of local stationarity for graph signals

In this paper, we extend the recent definition of graph stationarity into a definition of local stationarity. Doing so, we present a metric to assess local stationarity using projections on localized atoms on the graph. Energy of these projections defines the local power spectrum of the signal. We use this local power spectrum to characterize local stationarity and identify sources of non-stationarity through differences of local power spectrum. Finally, we take advantage of the knowledge of the spectrum of the atoms to give a new power spectrum estimator.

Local stationarity of graph signals: insights and experiments

In this paper, we look at one of the most crucial ingredient to graph signal processing: the graph. By taking a step back on the conventional approach using Gaussian weights, we are able to obtain a better spectral representation of a stochastic graph signal. Our approach focuses on learning the weights of the graphs, thus enabling better richness in the structure by incorporating both the distance and the local structure into the weights. Our results show that the graph power spectrum we obtain is closer to what we expect, and stationarity is better preserved when going from a continuous signal to its sampled counterpart on the graph. We further validate the approach on a real weather dataset.