We present a novel method for robust reconstruction of the image of a moving object from incomplete linear measurements. We assume that only few measurements of this object can be acquired at different instants and model the correlation between measurements using global geometric transformations represented by few parameters. Then, we design a method that is able to jointly estimate these transformation parameters and an image of the object, while taking into account possible occlusions of parts of the object during the acquisitions. The reconstruction algorithm minimizes a non-convex functional and generates a sequence of estimates converging to a critical point of this functional. Finally, we show how to apply this algorithm on a real cardiac acquisition for free breathing coronary magnetic resonance imaging.