  The forthcoming space-based gravitational wave observatory LISA will open a
new window for the measurement of galactic binaries, which will deliver
unprecedented information about these systems. However, the detection of
galactic binary gravitational wave signals is challenged by the presence of
gaps in the data. Whether being planned or not, gapped data dramatically reduce
our ability to detect faint signals and the risk of misdetection soars.
Inspired by advances in signal processing, we introduce a \nonparametric
inpainting algorithm based on the sparse representation of the galactic binary
signal in the Fourier domain. In contrast to traditional inpainting approaches,
noise statistics are known theoretically on ungapped measurements only. This
calls for the joint recovery of both the ungapped noise and the galactic binary
signal. We thoroughly show that sparse inpainting yields an accurate estimation
of the gravitational imprint of the galactic binaries. Additionally, we
highlight that the proposed algorithm produces a statistically consistent
ungapped noise estimate. We further evaluate the performances of the proposed
inpainting methods to recover the gravitational wave signal on a simple example
involving verification galactic binaries recently proposed in LISA data
challenges.
