基于截断核范数张量鲁棒主成分分析
Tensor Robust Principal Component Analysis Based on Truncated Nuclear Norm
DOI: 10.12677/AIRR.2020.92008, PDF,    科研立项经费支持
作者: 杨枥皓：西南大学数学与统计学院，重庆
关键词: 张量分解；主成分分析；截断核范数；图像去噪；Tensor Decomposition； Principal Component Analysis； Truncated Nuclear Norm； Image Denoising
摘要: 低管秩张量的分解由于其在图像处理中的实际应用已经在各个领域引起了关注。但是传统的张量分解算法为了得到给定张量的低秩和稀疏成分，利用了全部的数据。尽管这些现存的方法都有较快的收敛速度，但是这些方法都忽略了小奇异值几乎不含信息这一事实。基于这一事实，我们提出了一种新的分解方法。我们的方法通过限制核范数的大小从而简化张量分解。和其他张量恢复方法相较而言，我们提出的方法能在实验中能取得更好的效果。
Abstract: Low-tubal-rank tensor decomposition has been attracting attention of various fields due to the real application in image processing. However, conventional algorithms for tensor decomposition utilise the entire data to obtain the Low-tubal-rank and sparse components of a given tensor. Although many existing methods have fast convergence rates, these methods ignore the fact that small singular values contain little information. Based on this fact, we come up with a new decomposition method. Our method can simplify the tensor decomposition according to constrain the nuclear norm. Compared with the experimental results of many other tensor recovery methods, our proposed method can obtain a better effect.
文章引用：杨枥皓. 基于截断核范数张量鲁棒主成分分析[J]. 人工智能与机器人研究, 2020, 9(2): 64-73. https://doi.org/10.12677/AIRR.2020.92008

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