Non-convex super-resolution of oct images via sparse representation

We propose a non-convex variational model for the superresolution of Optical Coherence Tomography (OCT) images of the murine eye, by enforcing sparsity with respect to suitable dictionaries learnt from high-resolution OCT data. The statistical characteristics of OCT images motivate the use of -stable distributions for learning dictionaries, by considering the non-Gaussian case, = 1. The sparsity-promoting cost function relies on a non-convex penalty - Cauchy-based or Minimax Concave Penalty (MCP) - which makes the problem particularly challenging. We propose an efficient algorithm for minimizing the function based on the forward-backward splitting strategy which guarantees at each iteration the existence and uniqueness of the proximal point. Comparisons with standard convex `1-based reconstructions show the better performance of non-convex models, especially in view of further OCT image analysis.