Low-rank tensor recovery based on nonconvex logarithmic regularization factor

This paper studies the low-rank tensor recovery (LRTR) problem under the framework of tensor singular value decomposition (t-SVD). The t-SVD avoids the inherent information loss associated with tensor matricization. Conventional LRTR based on t-SVD approaches generally rely on nuclear norm minimization. However, in real-world applications, higher singular values are related to the most informative regions of an image. In light of this, we introduce an innovative nonconvex regularization term that treats different singular values of tensors distinctly. Aiming at the problem of pixel missing in the image, this paper introduces a new low-rank tensor completion model based on the nonconvex logarithmic regularization term. Besides, for the problem of the image denoising issue, this paper establishes a new tensor robust principal component analysis model. Two algorithms based on the alternating direction method of multipliers (ADMMs) are proposed to solve the proposed tensor recovery model. Experimental results on real images and videos demonstrate the superiority of the proposed model, especially in the aspect of denoising, where it exhibits significant advantages.