Gap interpolation by inpainting methods: Application to ground and space-based asteroseismic data

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 handling the problem, the so-called inpainting method. This technique, based on a prior condition of sparsity, enables the gaps in the data to be judiciously fill-in thereby preserving the asteroseismic signal as far as possible. The impact of the observational window function is reduced and the interpretation of the power spectrum simplified. This method is applied on both ground- and space-based data. It appears that the inpainting technique improves the detection and estimation of the oscillation modes. Additionally, it can be used to study very long time series of many stars because it is very fast to compute. For a time series of 50 days of CoRoT-like data, it allows a speed-up factor of 1000, if compared to methods with the same accuracy.