Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation

TL;DR

This paper introduces a novel tensor completion method using element-wise weighted low-rank tensor train with overlapping ket augmentation, effectively reducing blocking artifacts and improving recovery quality in high-order tensor data.

Contribution

The paper proposes a new tensor completion approach with element-wise weighting and overlapping ket augmentation, addressing limitations of existing TT-based methods.

Findings

Outperforms existing tensor completion methods in experiments.

Reduces blocking artifacts in high missing rate scenarios.

Improves recovery quality of edge elements.

Abstract

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor completion methods using TT decomposition have two obvious drawbacks. One is that they only consider mode weights according to the degree of mode balance, even though some elements are recovered better in an unbalanced mode. The other is that serious blocking artifacts appear when the missing element rate is relatively large. To remedy such two issues, in this work, we propose a novel tensor completion approach via the element-wise weighted technique. Accordingly, a novel formulation for tensor completion and an effective optimization algorithm, called as tensor completion by parallel weighted matrix factorization via tensor train (TWMac-TT), is proposed. In addition, we specifically consider the recovery quality of edge elements from adjacent blocks. Different from traditional reshaping and ket augmentation, we utilize a new tensor augmentation technique called overlapping ket augmentation, which can further avoid blocking artifacts. We then conduct extensive performance evaluations on synthetic data and several real image data sets. Our experimental results demonstrate that the proposed algorithm TWMac-TT outperforms several other competing tensor completion methods.