A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models

TL;DR

This paper introduces a novel variational framework using spatially-varying generalized Gaussian models for joint image reconstruction and feature extraction, demonstrating high-quality results in deblurring and segmentation tasks.

Contribution

It proposes a new non-convex variational formulation with space-variant Gaussian priors and an efficient alternating proximal algorithm with convergence analysis.

Findings

Achieves high-quality joint deblurring and segmentation results.

Effectively exploits structure of non-convex objective.

Demonstrates robustness in numerical experiments.

Abstract

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.