  In asteroseismology, the observed time series often suffers from incomplete
time coverage due to gaps. The presence of periodic gaps may generate spurious
peaks in the power spectrum that limit the analysis of the data. Various
methods have been developed to deal with gaps in time series data. However, it
is still important to improve these methods to be able to extract all the
possible information contained in the data. In this paper, we propose a new
approach to handle the problem, the so-called inpainting method. This
technique, based on a sparsity prior, enables to judiciously fill-in the gaps
in the data, preserving the asteroseismic signal, as far as possible. The
impact of the observational window function is reduced and the interpretation
of the power spectrum is simplified. This method is applied both on ground and
space-based data. It appears that the inpainting technique improves the
oscillation modes detection and estimation. Additionally, it can be used to
study very long time series of many stars because its computation is very fast.
For a time series of 50 days of CoRoT-like data, it allows a speed-up factor of
1000, if compared to methods of the same accuracy.
