Unified transformed t-SVD using unfolding tensors for visual inpainting

Low-rank tensor completion (LRTC) restores missing elements in multidimensional visual data; the challenge is representing the inherent structures within this data. Typical methods either suffer from inefficiency owing to the combination of multiple regularizers or perform suboptimally using inappropriate priors. In this study, we further investigated LRTC using tensor singular value decomposition (t-SVD). Inspired by the tensor–tensor product (t-product), we proposed a unified transformed t-SVD method that employs an invertible linear transform with a unitary transform matrix. However, the t-SVD-based framework lacks the flexibility necessary to represent different inherent relations along the tensor modes. To address this issue, we propose a tensor represented by a series of multidimensional unfolding tensors to fully explore the hidden structure of the original data. Furthermore, the proposed model can be solved efficiently using the alternate-direction method of the multiplier (ADMM) approach. Extensive experimental results on multidimensional visual data (multispectral images, hyperspectral images, and videos) demonstrated the superiority of the proposed method over other state-of-the-art LRTC-related methods.