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 a task of representing a matrix by a high-order-n tensor as that of encoding the matrix two-dimension (2D) indices (i, j) by n-digit words i1i2… in, we then 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 likes the ket augmentation of quantum physics, is capable of capturing all correlations and entanglements between entries of the original third order tensor. Accordingly, the resultant high-order tensor is completed by our previously developed parallel matrix factorization via tensor train. Simulations are provided to show the clear advantages of our approach to enhance important metrics of the 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.