Gabriele Scrivanti

Emilie Chouzenoux, Marie-Caroline Corbineau, Jean-Christophe Pesquet et al.

The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly propose a novel nonsmooth and non-convex variational formulation of the problem. For this purpose, we introduce a versatile generalised Gaussian prior whose parameters, including its exponent, are space-variant. Secondly, we design an alternating proximal-based optimisation algorithm that efficiently exploits the structure of the proposed non-convex objective function. We also analyse the convergence of this algorithm. As shown in numerical experiments conducted on joint deblurring/segmentation tasks, the proposed method provides high-quality results.

Gabriele Scrivanti, Luca Calatroni, Serena Morigi et al.

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 α-stable distributions for learning dictionaries, by considering the non-Gaussian case, α=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