Astrophysics has arrived to a turning point where the scientific exploitation of data requires overcoming challenging analysis issues, which mandates the development of advanced signal processing methods. In this context, sparsity and sparse signal representations have played a prominent role in astrophysics. Indeed, thanks to sparsity, an extremely clean full-sky map of the Cosmic Microwave Background (CMB) has been derived from the Planck data [Bobin14], a European space mission that observes the sky in the microwave wavelengths. This led to a noticeable breakthrough: we showed that the large-scale statistical studies of the CMB can be performed without having to mask the galactic centre anymore thanks to the achieved high quality component separation [Rassat14]. Despite the undeniable success of sparsity, standard linear signal processing approaches are too simplistic to capture the intrinsically non-linear properties of physical data. For instance, the analysis of the Planck data in polarization requires new sparse representations to finely capture the properties of polarization vector fields (e.g. rotation invariance), which cannot be tackled by linear approaches. Shifting from the linear to the non-linear signal representation paradigm is an emerging area in signal processing, which builds upon new connections with fields such as deep learning [Mallat13]. Inspired by these active and fertile connections, the LENA project will: i) study a new non-linear signal representation framework to design non-linear models that can account for the underlying physics, and ii) develop new numerical methods that can exploit these models. We will further demonstrate the impact of the developed models and algorithms to tackle data analysis challenges in the scope of the Planck mission and the European radio-interferometer LOFAR. We expect the results of the LENA project to impact astrophysical data analysis as significantly as deploying sparsity to the field has achieved.

Star formation is a fundamental process in astrophysics, which has been studied for decades. As of now, most of our knowledge is concentrated on the formation of stars of a few solar masses. If galaxies' total stellar mass is dominated by low-mass stars, their energy budget is exclusively controlled by the enormous luminosity and powerful feedback of massive stars (M > 8 Msun). Despite their importance, the mechanisms leading to the formation of high-mass stars remain a mystery in many aspects. From the theoretical point of view, low-mass star formation models are not directly transposable as they do not provide accretion rates in line with what is necessary for high-mass star formation. From the observational point of view, until the recent rise of large interferometers, little was known about the formation of massive stars due to their scarcity, and remoteness. Through my work with interferometers, I have proved that very dynamical processes (colliding flows) are at play in high-mass star-forming regions (HMSFR). On the other hand, recent studies have shown that magnetic fields are a key factor in the regulation of star-formation. I am convinced that the dynamical features observed in HMSFR coupled with the action of the magnetic fields could explain for the formation of high-mass stars. For this two-year project, I plan on studying the coupling of gas dynamics with magnetic fields. For this purpose, I present an innovative project that will study this coupling simultaneously from observational and numerical inquiries. I will use today's best instrument in radio-astronomy, ALMA, to trace both the kinematics of gas and the magnetic field morphology. This observational part relies on data that I have already acquired. For the numerical part, I will participate in the development of dedicated magneto-hydro-dynamical simulations together with P. Hennebelle to understand the physical processes that underlie the observational features.