In this paper, we propose new algorithms for estimating micro-vibrations and correcting its effects in satellite imaging with linear pushbroom camera. We first design an accurate model of the acquisition process with linear pushbroom camera, that incorporates the satellite attitude as parameters. We then propose a two stage reconstruction method based on an identification neural network to identify the attitude, followed by a deep unrolled network to correct the micro-vibrations. We then evaluate the proposed framework on synthetic and real data, showing promising results for this challenging problem. Our results highlight the critical role of the focal plane's geometry, to improve the micro-vibrations identifiability and therefore, the reconstruction quality.