论文标题
基于多模式核心张量分解基于低级别及其在张量完成的应用
Multi-mode Core Tensor Factorization based Low-Rankness and Its Applications to Tensor Completion
论文作者
论文摘要
低级张量的完成已被广泛用于计算机视觉和机器学习中。本文开发了一种新型的多模式核心张量分解（MCTF）方法，并结合了张量低级别度量和该量度的更好的非凸弛豫形式（NC-MCTF）。提出的模型编码了Tucker和T-SVD提供的一般张量的低级见解，因此有望在多个方向上同时模拟频谱低级别，并基于少数观察到的条目准确地恢复了固有的低级结构的数据。此外，我们研究MCTF和NC-MCTF正则化最小化问题，并设计有效的块连续的上限最小化（BSUM）算法来解决它们。该有效的求解器可以将MCTF扩展到各种任务，例如张量完成。一系列实验，包括高光谱图像（HSI），视频和MRI完成，证实了该方法的出色性能。
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.
