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.

翻译：图像复原与特征提取的联合问题是图像处理中的一项挑战性任务。该问题旨在以联合方式完成图像的重建及其特征提取。本文首先针对该问题提出一种新颖的非光滑非凸变分模型。为此，我们引入了一种灵活的广义高斯先验，其参数（包括指数）具有空间变化特性。其次，我们设计了一种基于交替近似的优化算法，该算法能够高效利用所提出的非凸目标函数的结构特性，并对其收敛性进行了分析。在联合去模糊/分割任务的数值实验中，所提方法展现了高质量的结果。