Employing low tensor rank decompositions in image inpainting has attracted increasing attention. This paper exploits a novel tensor-augmentation schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed augmentation schemes enhance the low-rankness of an image under three tensor decompositions: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solve the image inpainting problem with three low-rank con-strained models which use the matrix rank, TT rank, and tubal rank as constrained priors re-spectively. The tensor tubal rank and tensor train multi-rank are developed from t-SVD and TT decomposition respectively. We exploit efficient ADMM algorithms for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and supe-rior to numerous close methods.