Mathematical Challenges of the Euclid Spatial Project
Jean Luc Starck
CosmoStat Lab - CEA/Saclay
Weak gravitational lensing provides a unique way of mapping directly the dark matter in the universe. Gravitational lensing is the process in which light from distant galaxies is bent by the gravity of intervening mass in the universe as it travels towards us. The convergence field is derived from the gravitational shear of the background galaxy images.
The Euclid satellite is a very ambitious spatial mission selected by ESA and will be lanched in 2020. It will be able to map the large scale structure and weak lensing distortions out to high redshifts. Thanks to these shear measurements, we will be able to reconstruct a dark matter mass map of 15000 square degrees. We will review the different mathematical challenges related to the dark matter mass map reconstruction, and show how sparse representations could be very useful for analyzing the EUCLID data set. We will show that sparse recovery is indeed the right approach to reconstruct a 3D density mass field from galaxy shape measurements.