Tensor Completion via Linear Combination of Nuclear Norms

Tensor completion is commonly formulated by minimizing a convex combination of nuclear norms of mode-wise unfolding matrices. Although effective, the non-negative weight constraint can limit the flexibility of mode balancing, especially when different modes contribute unequally to the reconstruction. In this paper, we propose a tensor completion model based on a linear combination of nuclear norms, where the weights are allowed to take signed values under a normalization constraint. To implement this model, we develop an ADMM-based algorithm, termed FlexHaLRTC, which extends the standard singular value thresholding update to handle both shrinkage for positive weights and expansion for negative weights. Experiments on color image inpainting and video completion show that the proposed method achieves competitive PSNR, SSIM, and RSE results, with more noticeable gains in high-missing-rate settings.