An important task of data science is to represent and evidence the interrelation between coupled observables. The simple case of two observables that vary in time or space leads to bivariate signals. Those appear in virtually all fields of physical sciences, whenever two quantities of interest are related and jointly measured, such as in seismology (e.g. horizontal vs vertical ground motion), optics (transverse coordinates of the electric field), oceanography (components of current velocities), or underwater acoustics (horizontal vs vertical particle displacements) to cite a few.

Bivariate signals describe trajectories in a 2D plane whose geometric properties (e.g. directionality) have a natural interpretation in terms of the physical notion of polarization usually used for waves. As an example, according to Einstein’s theory of general relativity, the recently detected gravitational waves (GWs)
are characterized by two degrees of freedom, that are connected to the bivariate space-time strain signal measured by the detectors. The polarization state of the observed signal is directly connected to that of the wave, which in turn provides key insights into the underlying physics of the source. Polarization is thus a central concept for the analysis of bivariate signals.
Moreover, recent years have seen an increased interest in exploiting bivariate signals in many applications. For instance, in underwater acoustics, the advent of a new modality called IVAR capable of measuring particle velocity has opened promising avenues of research. Indeed, unlike conventional single-channel (e.g. pressure) sensors, these new vector sensors permit to probe the “geometry” of the underlying propagation medium. Thus, being able to fully take advantage of the information gathered in bivariate signals – notably, its polarization properties – is a crucial step towards understanding complex physical phenomena.
Unlocking these essential physical insights is bound to the development of new polarization-aware methodologies in bivariate signal processing. Including polarization information in the analysis and processing workflow is of general interest and can impact all elementary tasks in bivariate signal processing, namely analysis, modeling, filtering, detection, and statistical inference.
The RICOCHET project aims at establishing a complete set of theoretical and methodological tools to fully exploit the polarization information of bivariate signals. Their relevance will be extensively demonstrated on important practical problems arising in physical applications, notably gravitational-wave astronomy, underwater acoustics and seismology.