We propose a new model for the improved reconstruction of JPEG (Joint Photographic Experts Group) images. Given a JPEG compressed image, our method first determines the set of possible source images and then specifically chooses one of these source images satisfying additional regularity properties. This is realized by employing the recently introduced Total Generalized Variation (TGV) as regularization term and solving a constrained minimization problem. In order to obtain an optimal solution numerically, we propose a primal-dual algorithm. We have developed a parallel implementation of this algorithm for the CPU and the GPU, using OpenMP and Nvidia's Cuda, respectively. Finally, experiments have been performed, confirming a good visual reconstruction quality as well as the suitability for real-time application.