  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 misidentification call for the development of
robust methods. We describe here an original non-parametric reconstruction of
the imprint of galactic binaries in measurements affected by instrumental noise
typical of the space-based gravitational wave observatory LISA. We assess the
impact of various approaches based on sparse signal modelling and focus on
adaptive structured block sparsity. We carefully show that a sparse
representation gives a reliable access to the physical content of the
interferometric measurement. In particular we check the successful fast
extraction of the gravitational wave signal on a simple yet realistic example
involving verification galactic binaries recently proposed in LISA data
challenges.
