Data nowadays come in overwhelming volume. In order to cope with this deluge, we explore and use the benefits of geometry and symmetry in higher dimensional data. But volume is not the only problem: data models are also increasingly complex, mixing various components.
We thus use sparse representations and dictionaries as dimensionality reduction tools to dig out information from complicated high-dimensional datasets and multichannel signals, or to model complex behaviours in more classical signals.
Finally data can also be complex because they are collected on surfaces, or more generally manifolds, or because they are not scalar-valued. We thus explore extensions of Computational Harmonic Analysis in higher dimensions, in complex geometries, on graphs, networks or for non-scalar data.