Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme

Employing low tensor rank decomposition in image inpainting has attracted increasing attention. This study exploited novel tensor arrangement schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed arrangement schemes enhanced the low rankness of images under three tensor decomposition methods: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solved the image inpainting problem with three low-rank constrained models that use the matrix rank, TT rank, and tubal rank as constrained priors. The tensor tubal rank and tensor train multi-rank were developed from t-SVD and TT decomposition, respectively. Then, ADMM algorithms were efficiently exploited for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and superior to numerous close methods.