Low-rank tensor completion based on tensor train rank with partially overlapped sub-blocks and total variation

Recently, the low-rank tensor completion method based on tensor train (TT) rank has achieved promising performance. Ket augmentation (KA) is commonly used in TT rank-based methods to improve the performance by converting low-dimensional tensors to higher-dimensional tensors. However, block artifacts are caused since KA also destroys the original structure and image continuity of original low-dimensional tensors. To tackle this issue, a low-rank tensor completion method based on TT rank with tensor augmentation by partially overlapped sub-blocks (TAPOS) and total variation (TV) is proposed in this paper. The proposed TAPOS preserves the image continuity of the original tensor and enhances the low-rankness of the generated higher-dimensional tensors, and a weighted de-augmentation method is used to assign different weights to the elements of sub-blocks and further reduce the block artifacts. To further alleviate the block artifacts and improve reconstruction accuracy, TV is introduced in the TAPOS-based model to add the piecewise smooth prior. The parallel matrix decomposition method is introduced to estimate the TT rank to reduce the computational cost. Numerical experiments show that the proposed method outperforms the existing state-of-the-art methods.