Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2016, Vol. 45(6): 840-860
“纪念《数学进展》创刊六十周年”特约综述文章
图像与视频处理的张量方法
Tensor Approach for Image and Video Processing

彭立中1,张帆1,周丙寅2
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


PDF
[524 KB]
926
下载
396
浏览

引用导出
0
    /   /   推荐

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  
[1] Benson, C., Dooley, A.H. and Ratcliff, G., Fundamental solutions for powers of the Heisenberg sub-Laplacian, Illonis J. Math., 1993, 37(3): 455-476.
[2] Bonfiglioli, A., Lanconelli, E. and Uguzzoni, F., Stratified Lie Groups and Potential Theory for Their Sub-Laplacians,Springer Monogr. Math., Berlin: Springer-Verlag, 2007.
[3] Courant, R. and Hilbert, D., Methods of Mathematical Physics, Volume II, New York: Interscience Publishers, 1966, 275-279.
[4] Folland, G.B., Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., 1975, 13(1/2): 161-207.
[5] Folland, G.B. and Stein, E.M., Estimates for the $\overline{\partial_b complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 1974, 27(4): 429-522.
[6] Han, Y.Z., Niu, P.C. and Luo, X.P., A Hardy type inequality and indefinite eigenvalue problems on the homogeneous group, J. Partial Differ. Equ., 2002, 15(4): 28-38.
[7] H\"{o}rmander, L. and Melin, A., Free systems of vector fields, Ark. Mat., 1978, 16(1/2): 83-88.
[8]罗学波, 钮鹏程, 韩亚洲, 拟齐性偏微分算子的分析, 西安: 西北工业大学出版社, 2007.
[9] Rothschild, L.P. and Stein, E.M., Hypoelliptic differential operators and nilpotent groups, Acta Math., 1976, 137(1): 247-320.
No related articles found!
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .