Accurate regularized Tucker decomposition for image restoration

We propose a new accurate regularized Tucker decomposition (ARTD) method for image restoration (IR), which considers global low-rankness and local similarity of intrinsic image characteristics. Specifically, global low-rankness is represented by a sparse Tucker core tensor, whereas the local similarity is captured using nonnegative factor matrices and manifold regularization terms. Sparse nonnegative Tucker decomposition (SNTD) and graph nonnegative Tucker decomposition (GNTD) can be considered a special case of ARTD. We propose and implement an effective Alternating Proximal Gradient (APG) based algorithm to solve the ARTD model and deduce the closed-form updating rules. Notably, ARTD does not need to tune the Tucker rank and provides an initialization strategy and a first-order feedback control rule to accelerate its convergence. Experiments on real IR problems show that our method outperforms some existing state-of-the-art methods.& COPY; 2023 Elsevier Inc. All rights reserved.