Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completion

About

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally demanding. In addition, the determination of the optimal TR rank is a tough work in practice. To overcome these drawbacks, we first introduce a class of new tensor nuclear norms by using tensor circular unfolding. Then we theoretically establish connection between the rank of the circularly-unfolded matrices and the TR ranks. We also develop an efficient tensor completion algorithm by minimizing the proposed tensor nuclear norm. Extensive experimental results demonstrate that our proposed tensor completion method outperforms the conventional tensor completion methods in the image/video in-painting problem with striped missing values.

Jinshi Yu, Chao Li, Qibin Zhao, Guoxu Zhou · 2019

Related benchmarks

Task	Dataset	Result
Low-Rank Tensor Completion	MRSIs SR=1% (test)	MPSNR19.99	15
Tensor completion	Face datasets (0.3% Sampling Rate)	MPSNR20.26	15
Tensor completion	Face datasets 3% Sampling Rate	MPSNR29.99	15
Low-Rank Tensor Completion	MRSIs SR=0.5% (test)	MPSNR17.25	15
Tensor completion	Face datasets 0.5% Sampling Rate	MPSNR22.44	15
Tensor completion	Face datasets 1% Sampling	MPSNR25	15
Low-Rank Tensor Completion	MRSIs SR=3% (test)	MPSNR22.35	15
Low-Rank Tensor Completion	MRI Sampling Rate 0.1%	MPSNR19.19	15
Tensor completion	Face datasets 0.1% Sampling Rate	MPSNR14.33	15
Low-Rank Tensor Completion	MRSIs SR=5% (test)	MPSNR23.66	15