The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10-15 precision. Reaching this performance requires an accurate and robust data analysis method, especially since the possible WEP violation signal will be dominated by a strongly colored noise. An important complication is brought by the fact that some values will be missing—therefore, the measured time series will not be strictly regularly sampled. Those missing values induce a spectral leakage that significantly increases the noise in Fourier space, where the WEP violation signal is looked for, thereby complicating scientific returns. Recently, we developed an inpainting algorithm to correct the MICROSCOPE data for missing values. This code has been integrated in the official MICROSCOPE data processing and analysis pipeline because it enables us to significantly measure an equivalence principle violation (EPV) signal in a model-independent way, in the inertial satellite configuration. In this work, we present several improvements to the method that may allow us now to reach the MICROSCOPE requirements for both inertial and spin satellite configurations. The main improvement has been obtained using a prior on the power spectrum of the colored noise that can be directly derived from the incomplete data. We show that after reconstructing missing values with this new algorithm, a least-squares fit may allow us to significantly measure an EPV signal with a 0.96 ×10-15 precision in the inertial mode and 1.20 ×10-15 precision in the spin mode. Although, the inpainting method presented in this paper has been optimized to the MICROSCOPE data, it remains sufficiently general to be used in the general context of missing data in time series dominated by an unknown colored noise. The improved inpainting software, called inpainting for colored-noise dominated signals, is freely available at http://www.cosmostat.org/software/icon.