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J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> 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. 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