Optical coherence tomography (OCT) is an essential medical imaging tool for retinal disease diagnosis. Nevertheless, as with all optical imaging techniques, image degradation is a very common phenomenon, affecting the quality of the images. In this paper, we address issues related to the resolution of OCT images and propose solutions based on solving inverse problems. A cost function for deconvolution and super-resolution is formulated and the alternating direction method of multiplier (ADMM) and forward-backward splitting (FBS) algorithms are then employed for its minimisation. On the one hand, the standard Ll norm regularisation with soft thresholding is compared with a total variation (TV) regularisation within an ADMM scheme. On the other hand, nonconvex regularisation is also considered via a multivariate generalisation of the minimax-concave scheme in FBS. In the latter case, the regularisation function is judiciously chosen in order to preserve the overall convexity of the cost function. To be able to evaluate our algorithms qualitatively, a number of standard images are initially used. Then, we also assess our algorithms subjectively by applying them to real OCT images of the human eye. Given that the point spread function (PSF) of OCT images is generally unknown, we also propose ways of estimating it in the deconvolution component of our methods. Our results show that the ADMM scheme with soft thresholding achieves the best performance in terms of enhancing the overall quality of OCT images.