Multi-mode Tensor Singular Value Decomposition for Low-Rank Image Recovery

Tensor completion aims to recover the missing entries in multi-way data. Based on the low-rank assumption, many methods according to different tensor decomposition frameworks have been developed for image recovery. Recently emerging tensor singular value decomposition (t-SVD) can better characterize the low-rank structure for 3rd-order data, but it suffers from rotation sensitivity and demands for a higher-order version. As the high-order extension of matrix SVD, Tucker decomposition tries to extract low-rank information along each mode. Inspired by this, we extend t-SVD into an improved one called multi-mode tensor singular value decomposition, which can explore the low-rank information along different modes. Based on it, a convex multi-dimensional square model for tensor completion is proposed and solved by the classic alternating direction method of multipliers. Experimental results on color image and multispectral image completion demonstrate the superior recovery accuracy and competitive CPU time of our method compared with existing state-of-the-art ones.