Sparsity-based recovery of Galactic-binary gravitational waves

The detection of Galactic binaries as sources of gravitational waves promises an unprecedented wealth of information about these systems but also raises several challenges in signal processing. In particular the large number of expected sources and the risk of misdetection call for the development of robust methods. We describe here an original nonparametric recovery of the imprint of Galactic binaries in measurements affected by instrumental noise typical of the space-based gravitational wave observatory LISA. This method, based on a denoising procedure, aims at separating from noise the sum of all signals coming from Galactic binaries. We assess the impact of various approaches based on sparse signal modeling and focus on adaptive structured block sparsity. We carefully show that a sparse representation of the interferometric measurement gives a reliable access to the total signal coming from Galactic binaries. In particular we check the successful fast recovery of the gravitational wave signal on a simple yet realistic example involving verification Galactic binaries recently proposed in LISA data challenges.