  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.
