A non-convex low-rank image decomposition model via unsupervised network

Image decomposition is the separation of a given image into two parts with different features, i.e., structure and texture. In order to extract the image information comprehensively, a non-convex unsupervised image decomposition model is proposed in this paper. Firstly, we propose a new non-convex low-rank regular term to describe the low-rank nature of images, which focuses on optimizing the sum of partial singular values of image matrices using a non-convex truncated nuclear norm. Secondly, unsupervised network is used to capture image information by learning the deep semantic information of the image and then extracting the image structure. Finally, the alternative direction method of multipliers is used to divide the model into three sub-problems and optimize them separately. For the non-convex sub-problem, a two-stage solution scheme is given by employing the singular value decomposition technique, and experimental analysis is carried out on both real and synthetic images. The experimental results show that the proposed non-convex image decomposition method outperforms other state-of-the-art methods in terms of subjective visual effects. Meanwhile, in the quantitative evaluation, the proposed method shows a large improvement compared with other methods, with a maximum improvement of 15 % in the structural similarity index measure (SSIM) index.