To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data
  Completion
Le Xu Lei Cheng Ngai Wong Yik-Chung Wu
Tensor train (TT) representation has achieved tremendous success in visual
data completion tasks, especially when it is combined with tensor folding.
However, folding an image or video tensor breaks the original data structure,
leading to local information loss as nearby pixels may be assigned into
different dimensions and become far away from each other. In this paper, to
fully preserve the local information of the original visual data, we explore
not folding the data tensor, and at the same time adopt graph information to
regularize local similarity between nearby entries. To overcome the high
computational complexity introduced by the graph-based regularization in the TT
completion problem, we propose to break the original problem into multiple
sub-problems with respect to each TT core fiber, instead of each TT core as in
traditional methods. Furthermore, to avoid heavy parameter tuning, a sparsity
promoting probabilistic model is built based on the generalized inverse
Gaussian (GIG) prior, and an inference algorithm is derived under the
mean-field approximation. Experiments on both synthetic data and real-world
visual data show the superiority of the proposed methods.