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数学进展 - 2016, Vol. 45(6): 840-860
Tensor Approach for Image and Video Processing

PENG Lizhong1,ZHANG Fan1,ZHOU Bingyin2

1. 北京大学数学科学学院, 北京, 100871;
2. 河北师范大学数学与信息科学学院, 石家庄, 河北, 050024
1. School of Mathematical Sciences, Peking University, Beijing, 100871,P. R. China;
2. College of Mathematics and Information Sciences,Hebei Normal University, Shijiazhuang, Hebei, 050024, P. R. China

收稿日期: 2016-04-26
出版日期: 2016-11-10
2016, Vol. 45(6): 840-860
DOI: 10.11845/sxjz.2016002a

[524 KB]

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摘要 最近研究表明, 张量是多维数据的自然表示形式, 能够保持数据的内在结构,而张量分解和特征值分析是处理和分析高维数据的潜在工具.张量的数学基础和基于张量的数据分析技术都得到了极大发展.本文对高阶张量分析及其在图像和视频处理中的应用进行综述,并指出一些可能的研究问题.
Abstract:Recently, it has been revealed that tensors are natural representations of multidimensional data preserving their intrinsic structure, and tensor decomposition and eigenvalue analysis are potential tools to process and analyze such data. The mathematical foundation of tensor has been developing rapidly as well as tensor-based data analysis techniques. In this paper, we present a survey on higher-order tensor analysis and their applications in the field of image and video processing.We also indicate some problems for further research.
PACS:  O151.23  
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