SCTV-TC: Schatten p-Norm and Correlated Total Variation for Tensor Completion

Tensor completion (TC) is a critical task in various fields, including computer vision, remote sensing, and data analysis, due to the frequent occurrence of missing values and noise in multi-dimensional data. Traditional methods such as Tensor Nuclear Norm (TNN) and Tensor Robust Principal Component Analysis (TRPCA) have made significant progress, but face challenges in efficiency and accuracy, especially for high-dimensional data sets. In this paper, we propose an improved TC method, SCTV-TC, which integrates the Schatten <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-norm and the Correlated Total Variation (CTV). The Schatten <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-norm provides a more balanced penalisation of singular values, avoiding the bias introduced by uniform shrinkage in nuclear norm methods. The CTV preserves local smoothness and continuity, enhancing the robustness of the completion process. We use the Alternating Direction Method of Multipliers (ADMM) for optimisation, ensuring scalability and efficiency. Extensive experiments on hyperspectral image inpainting show that SCTV-TC outperforms state-of-the-art methods in terms of PSNR, SSIM, FSIM, ERGAS and MSAM, with particular excellence in the ERGAS metric. These results confirm the effectiveness of SCTV-TC in handling high-dimensional and complex data with missing values.