Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2020-2021)

Using data to benefit humanity is a grand challenge for today's engineers and data scientists (e.g., via environmental monitoring, improving public health, and sustainability). This research program aims to develop novel signal processing theory and methods to address challenges associated with processing and learning from unstructured or irregularly-sampled data. Existing signal processing techniques are well-suited for data such as time series and images which have a regular, well-ordered domain. Many contemporary applications produce data that is massive, complex, and unstructured. Graphs provide a principled formalism to capture complex relationships among variables and entities. In some applications the graph may capture a physical structure underlying the signal (e.g., traffic intensities on links of a road network, demand signals at nodes of the smart grid, or a measure of people's opinions in a social network). Graphs may also serve as a useful means to encode which data sampling locations we expect to produce similar values when signals are sampled irregularly in space and/or time (e.g., EEG and/or MRI signals sampled on the surface of the brain, or a network of sensors spread irregularly over a region). In other applications, where the graph is not directly apparent, it may encode logical relationships among entities (e.g., correlative, causal, or otherwise influential relationships). In this case it is often of interest to infer a graph from the observations in order to better understand the structure, organization, and function of a complex system.

This research program will make contributions to the burgeoning field of graph signal processing. The specific objectives of the proposed program are organized along three thrusts. (1) We will develop novel theory and methods for inferring graphs from signals under models where the signals are assumed to be smooth over the graph. In cases where signals cannot be observed at every vertex, we will infer structural or statistical properties of the graph that may still be useful for other applications like sampling. (2) We will develop novel theory and methods for approximating and compressing graph signals. While the theories of sampling and filtering graph signals are becoming more mature, little is known about what conditions on the signal-generating process and the graph structure are necessary for the resulting signal to be smooth or otherwise parsimoniously representable. The theoretical results will facilitate quantifying the tradeoff between the number of coefficients used to represent (i.e., approximate or compress) a graph signal and the resulting error incurred, given a family of graphs and graph signals. (3) We will develop methods for tracking in high-dimensional non-linear/non-Gaussian state-space models and sampling/filtering graph signals that exploit graph structure to improve computational efficiency.