Efficient image/video storage and transmission on mobile devices is becoming today an important challenge, since smartphones have become the most popular image acquisition devices, progressively replacing traditional cameras. However, most of the time, the acquired pictures are displayed on small screens and for a limited time. In order to manage this kind of oversized (with respect to the usage) data, it is mandatory to employ dedicated compression techniques. The solution considered in this article consists of storing solely low resolution versions of the images that can be efficiently compressed with standardized solutions. The challenge is then to restore high quality, full resolution images, while dealing with the complex artifacts that are inherently introduced by modern codecs. In this article, we introduce a two-stage approach, which consists of applying a deep superresolution technique upon images compressed with state-of-the-art codecs. The experimental results obtained demonstrate that the proposed method outperforms, in terms of perceptual quality, existing compression standards, in particular at very low bitrates.