Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a tensor low-rank decomposition method together with a tensor low-rankness measure (MCTF) and a better nonconvex relaxation form of it (NonMCTF). This is the first method that can accurately restore the clean data of intrinsic low-rank structure based on few known inputs. This metric encodes low-rank insights for general tensors provided by Tucker and T-SVD. Furthermore, we studied the MCTF and NonMCTF regularization minimization problem, and designed an effective BSUM algorithm to solve the problem. This efficient solver can extend MCTF to various tasks, such as tensor completion and tensor robust principal component analysis. A series of experiments, including hyperspectral image (HSI) denoising, video completion and MRI restoration, confirmed the superior performance of the proposed method

翻译：在计算机视觉和机器学习中,广泛使用低级高压完成率的方法。本文开发了一种高压低级分解方法,同时开发了高压低级测量(MCTF)和更好的非混凝解放松形式(UNMCTF)。这是能够准确恢复基于鲜为人知的投入的内在低级结构的清洁数据的第一个方法。这套指标编码了塔克和T-SVD为普通高压者提供的低级洞察力。此外,我们研究了MCTF和非MTF将问题降到最低,并设计了一个有效的BSUM算法来解决问题。这个高效的解算器可以将MCTF扩大到多种任务,例如高压完成率和强势本件分析。一系列实验,包括超光谱图像的消散、视频完成和MRI恢复,证实了拟议方法的出色表现。