Missing data are a common problem in experimental and observational physics. They can be caused by various sources, such as an instrument’s saturation, a contamination from an external event, or a data loss. In particular, they can have a disastrous effect when one is seeking to characterize a colored-noise-dominated signal in Fourier space, since they create a spectral leakage that can artificially increase the noise. It is therefore important to either take them into account or to correct for them prior to, e.g., a least-square fit of the signal to be characterized. In this paper, we present an application of the inpainting algorithm to mock MICROSCOPE data. Inpainting is based on a sparsity assumption, and has already been used in various astrophysical contexts; MICROSCOPE is a French Space Agency mission (whose launch is expected in 2016) that aims to test the weak equivalence principle down to the $10^{-15}$ level. We then explore the inpainting dependence on the number of gaps and the total fraction of missing values. We show that, in a worst-case scenario, after reconstructing missing values with inpainting a least-square fit may allow us to significantly measure a $1.1\times {10}^{-15}$ equivalence principle violation signal, which is sufficiently close to the MICROSCOPE requirements to implement inpainting in the official MICROSCOPE data processing and analysis pipeline. Together with the previously published KARMA method, inpainting will then allow us to independently characterize and cross-check an equivalence principle violation signal detection down to the $10^{-15}$ level.

• Received 17 September 2015

DOI:https://doi.org/10.1103/PhysRevD.92.112006