We propose a new model for the improved reconstruction and zooming of JPEG (Joint Photographic Experts Group) images. In the reconstruction process, 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. Data fidelity is modeled by the composition of a color-subsampling and a discrete cosine transformation operator. Furthermore, extending the notion of data set by allowing unconstrained intervals, the method facilitates optional magnification of the original image. 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 Nvidias Cuda, respectively. Finally, experiments have been performed, confirming a good visual reconstruction quality as well as the suitability for real-time application.