This paper introduces a new approach to single-image super-resolution in Optical Coherence Tomography (OCT) images. Retinal OCT images can be used to diagnose various diseases, not only peculiar to the eye, but also some systemic diseases. Nevertheless, as with any imaging modality, the acquired images suffer from degradation due to various causes. To overcome this and enhance image quality, Super-Resolution (SR) techniques are widely used. This work explores a convex regularization approach based on a multivariate generalization of the minimax-concave (GMC) scheme in a forward-backward splitting (FBS) scheme. Based on the assumption that sparse representations of OCT images are heavy-tailed, an α-stable dictionary is employed. This approach is implemented with overlapping and non-overlapping patches. Since the Point Spread Function (PSF) of the images used is generally unknown, it is estimated using a method originally proposed for ultrasound images. The algorithm is tested on OCT images of murine eyes. The results show that the proposed convex regularization method provides results that are competitive with the state-of-the-art. Indeed, significant deblurring and quality enhancement are achieved using the proposed algorithm and in most cases it provides the best results, both objectively and subjectively.