Super-resolved image enhancement is of great importance in medical imaging. Conventional methods often require multiple low resolution (LR) images from different views of the same object or learning from large amount of training datasets to achieve success. However, in real clinical environments, these prerequisites are rarely fulfilled. In this paper, we present a self-learning based method to perform superresolution (SR) from a single LR input. The mappings between the given LR image and its downsampled versions are modeled using support vector regression on features extracted from sparse coded dictionaries, coupled with dual-tree complex wavelet transform based denoising. We demonstrate the efficacy of our method in application of cardiac MRI enhancement. Both quantitative and qualitative results show that our SR method is able to preserve fine textural details that can be corrupted by noise, and therefore can maintain crucial diagnostic information.