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

TL;DR

This paper introduces a non-convex variational model for super-resolution of OCT images using sparsity with learned dictionaries, demonstrating improved performance over traditional convex methods.

Contribution

It presents a novel non-convex sparsity-promoting model and an efficient algorithm for OCT image super-resolution, leveraging ta-stable distributions for dictionary learning.

Findings

Non-convex models outperform convex L1-based methods in OCT super-resolution.

The proposed algorithm guarantees convergence with unique proximal points.

Enhanced OCT image quality facilitates better subsequent analysis.

Abstract

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