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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.
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To further de
Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the data. Missing
Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due to the mu
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonio