Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data

• Published in: Journal of mathematical imaging and vision Vol. 62; no. 6-7; pp. 900 - 918
• Main Authors: Lin, Xue-Lei, Ng, Michael K., Zhao, Xi-Le
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2020; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Color imagery; Computer Science; Factorization; Image Processing and Computer Vision; Mathematical analysis; Mathematical Methods in Physics; Optimization; Redundancy; Regularization; Signal,Image and Speech Processing; Smoothness; Tensors; Tensor completion; 90C30; 65F22; Tensor factorization; Proximal alternating minimization; 90C90; Hybrid regularization; 90C26
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-019-00933-9

The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two factor tensors) can be used to approximate such tensor very well. Motivated by the spatial/temporal smoothness of factor tensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization model for low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm. Numerical results on color images, color videos, and multispectral images are reported to illustrate the superiority of the proposed method over competing methods.