As an important tracer of the matter in the universe, galaxy surveys are commonly used to study the matter distribution. However, these surveys present several problems. First they are subject to shot noise (i.e. Poisson noise, because they are counting maps), secondly most of the data in the galactic plane cannot be trusted or is unavailable and missing data have to be properly taken into account. As we focus on medium scales, we assume that the matter overdensity, and so the galaxy overdensity, follow a log-normal distribution. Using a data augmentation framework, we propose a two-steps method for both denoising and inferring the missing data (inpainting). We begin by filling the missing data of the observation with a texture synthesis algorithm that try to preserve the observed data and the assumed power spectra. As the texture synthesis is random, we can generate several complete observations (multiple imputations). Then, as we have completed observation, we estimate the galaxy overdensity using a MAP estimator with a log-normal prior and support preservation. Preliminary results are showed using both synthesis and real dataset. Finally, some extension are proposed where we learn information needed to estimate the overdensity and fill the missing data, while still keeping a strong link the theory.