  Tensor completion estimates missing components by exploiting the low-rank
structure of multi-way data. The recently proposed methods based on tensor
train (TT) and tensor ring (TR) show better performance in image recovery than
classical ones. Compared with TT and TR, the projected entangled pair state
(PEPS), which is also called tensor grid (TG), allows more interactions between
different dimensions, and may lead to more compact representation. In this
paper, we propose to perform image completion based on low-rank tensor grid. A
two-stage density matrix renormalization group algorithm is used for
initialization of TG decomposition, which consists of multiple TT
decompositions. The latent TG factors can be alternatively obtained by solving
alternating least squares problems. To further improve the computational
efficiency, a multi-linear matrix factorization for low rank TG completion is
developed by using parallel matrix factorization. Experimental results on
synthetic data and real-world images show the proposed methods outperform the
existing ones in terms of recovery accuracy.
