Qualitative HD Image and Video Recovery via High-Order Tensor Augmentation and Completion

This paper presents a new framework for severely distorted image and video recovery via tensor augmentation and completion. By considering the task of representing a matrix by a high-order-$n$ tensor as that of encoding the matrix's 2-D indices $(i,j)$ by $n$-digit words $i_1i_2\dots i_n$, we develop a new high order tensor augmentation to cast a third order tensor of color images or video sequences containing missing pixels into a higher order tensor, which is similar to the ket augmentation of quantum physics, is capable of capturing all correlations and entanglements between entries of the original third order tensor. Accordingly, the resuling high-order tensor is completed by our previously developed parallel matrix factorization via tensor train decomposition. Simulations are provided to show the clear advantages of our approach in enhancing important metrics of visual quality such as relative square error and structural similarity index in image and video processing that help to achieve high recovery rates even for high-definition images and videos with 95% missing pixels.