Non-convex Super-resolution of OCT images via sparse representation

Gabriele Scrivanti (1) , Luca Calatroni (2) , Serena Morigi (1) , Lindsay Nicholson (3) , Alin Achim (3)

1 Dipartimento di Matematica [Bologna]
2 MORPHEME - Morphologie et Images
3 University of Bristol [Bristol]

We propose a non-convex variational model for the super-resolution 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 {\alpha}-stable distributions for learning dictionaries, by considering the non-Gaussian case, {\alpha}=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 L1-based reconstructions show the better performance of non-convex models, especially in view of further OCT image analysis

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Traitement des images [eess.IV]

Gabriele Scrivanti, Luca Calatroni, Serena Morigi, Lindsay Nicholson, Alin Achim. Non-convex Super-resolution of OCT images via sparse representation. 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), Apr 2021, Nice, France. ⟨hal-02978016⟩