  Missing data are a common problem in experimental and observational physics.
They can be caused by various sources, either an instrument's saturation, or 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 {\it inpainting} algorithm to mock MICROSCOPE data; {\it
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 {\it 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
{\it inpainting}, a Least-Square fit may allow us to significantly measure a
$1.1\times10^{-15}$ Equivalence Principle violation signal, which is
sufficiently close to the MICROSCOPE requirements to implement {\it inpainting}
in the official MICROSCOPE data processing and analysis pipeline. Together with
the previously published KARMA method, {\it inpainting} will then allow us to
independently characterize and cross-check an Equivalence Principle violation
signal detection down to the $10^{-15}$ level.
