ASTRES : Analysis, Synthesis and Transformations by Reassignment, EMD and Synchrosqueezing

Disentangling multicomponent signals and images into elementary constitutive parts is an important problem because of its ubiquity in many areas of science and technology. This however remains a challenging question for different reasons. On the one hand, there is no unique definition of what « multicomponent » means. On the other hand, we are now overwhelmed by a « deluge » of data and the question of extracting useful information from them has taken new forms. One facet of this proliferation is that getting more data often means facing extended variabilities, with a reduced hope that « universal » methods would be equally efficient in every context. This suggests a move towards more adaptive, ideally data-driven, methods, and it is precisely within this framework that ASTRES is proposed, with the underlying idea that, in a situation where data can now be quantitatively abundant, tailoring methods to individual specificities should add some significant extra value to the result of their processing.

More specifically, ASTRES will focus on advanced data-driven signal and image processing techniques aimed at disentangling complicated, nonstationary waveforms and fields into a small number of physically meaningful components. This will be achieved by exploiting local data structure (and in particular phase information) to get improved analysis, synthesis, and processing schemes.

Addressing those issues calls for a cooperation of advanced techniques in signal and image processing as well as in applied mathematics, with emphasis on recent optimization methods. This is reflected by the structure of the ASTRES collaboration, which relies on three teams chosen for their acknowledged expertise and complementarity. As for its scientific content, ASTRES is organized around three main techniques of multicomponent signal and image decomposition, namely the « reassignment method » (aimed at providing sharply peaked time-frequency representations), the « synchrosqueezing transform » (which also operates in a transformed domain—time-frequency or time-scale plane—, with a further sake of component reconstruction) and the « Empirical Mode Decomposition » (which directly works in the observation space, but with a similar purpose of component estimation). Those techniques, which share a number of common features—either in their form or in their goals—have attained different levels of maturity. The purpose of ASTRES will be to construct equally sound theoretical frameworks for them, as well as unified frameworks and efficient algorithms. The current status of the methods will be considered as a starting point, paving the way for numerous extensions to more complex settings, in particular multivariate and multidimensional. Finally, one ambition of the ASTRES project is to make the newly developed techniques become an entire part of processing schemes, beyond the sole analysis (or, sometimes, synthesis) tasks for which they have been used so far. In this respect, while ASTRES is mostly a methodological project, it will be both fed by and confronted to specific application areas, in particular in audio, physics and biomedicine.