Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex relaxation form of this measure (NC-MCTF). The proposed models encode low-rank insights for general tensors provided by Tucker and T-SVD, and thus are expected to simultaneously model spectral low-rankness in multiple orientations and accurately restore the data of intrinsic low-rank structure based on few observed entries. Furthermore, we study the MCTF and NC-MCTF regularization minimization problem, and design an effective block successive upper-bound minimization (BSUM) algorithm to solve them. This efficient solver can extend MCTF to various tasks, such as tensor completion. A series of experiments, including hyperspectral image (HSI), video and MRI completion, confirm 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声压完成率,本文开发了一种新型的多式核心感应因子化(MCTF)方法,结合一种低声调的低声调测量法和这一措施的更好的非电解放松形式(NC-MCTF)。拟议的模型将塔克和T-SVD提供的普通感应器的低声感知编码为低声调,因此预计将同时在多个方向上模拟光谱低声调,并精确恢复以少数观测到的条目为基础的内在低声层结构的数据。此外,我们研究了MCTF和NC-MTF的标准化最小化问题,并设计了一条有效的区块连续的上限最小化(BSUM)算法来解决这些问题。这个高效的求解器可以将MCTF扩大到多种任务,如多声道完成。一系列实验,包括超光谱图像(HSI)、视频和MRI完成,证实了拟议方法的优异性表现。