The problem of data storage and transmission on mobile devices is constantly growing up. Smartphones are nearly by default equipped with HD cameras that are taking high quality pictures, which can be instantly stored and easily uploaded on cloud platforms. Such a behavior favors the creation of a massive amount of data. In order to reduce the size of such data, it is mandatory to dispose of efficient compression techniques that can take into account the actual usage of such image data. For example, most of the pictures acquired by phone cameras are often displayed on a small screen and this, for a little amount of time. A solution to manage this kind of oversized data would be to store them in a lower resolution, additionally to a standard image compression. The downside of such an approach is that restoring an image to its original resolution is a challenging task, notably in the presence of complex compression artifacts, such as those introduced by sophisticated compression methods. In order to deal with such an issue, in this paper we propose a new model, specifically trained to perform super-resolution after compression with the BPG state-of-the-art codec. An advantage of the proposed approach comes from the fact that the underlying process can be interpreted as a postprocessing step, which can be easily added to any compression scheme without modifying the codec. Experimental results show that our model perceptually outperforms the state-of-the-art compression standards even for very low bitrates.