Magnetic resonance imaging can only acquire volume data with finite resolution due to various factors. In particular, the resolution in the slice direction is much lower than that in the in-plane direction, yielding un-realistic visualizations. To solve this problem, interpolation techniques have conventionally been applied. However, classical interpolation techniques generally cause some artifact noise such as jaggedness and blurring in the edge regions. In this paper, we propose a new superresolution framework for generating high-resolution data in the slice direction. In the proposed approach, we estimate the high-frequency component using a learning-based super-resolution technique with sparse representation and prove that the dictionary can be constructed using the in-plane frame as the input data without any other high-resolution data as training. Furthermore, we optimize estimated high-resolution data by adding a new regularization term with a nonlocal means algorithm. Experiments confirm that our proposed method is more effective than the conventional methods.