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.

中文翻译：

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具有总变化量的Tensor因式分解和Tikhonov正则化用于成像数据中的低秩张量完成

本文的主要目的是研究张量分解以降低成像数据中的低秩张量。由于现实世界中成像数据的潜在冗余，可以使用低管形张量张量分解（两个因子张量的张量-张量积）很好地近似这种张量。基于现实世界成像数据中因子张量的时空平滑性，我们建议将总变化量和Tikhonov正则化相结合的混合正则化方法用于低秩张量完成问题的低管形张量因子分解模型中。我们还开发了一种有效的近端交替最小化（PAM）算法，以解决相应的最小化问题并建立PAM算法的全局收敛性。彩色图像，彩色视频的数值结果，