图像与视频处理的张量方法（英文）  

Tensor Approach for Image and Video Processing

作　　者：彭立中[1] 张帆[1] 周丙寅[2] 

机构地区：[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

出　　处：《数学进展》2016年第6期840-860,共21页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11301137,No.11371036);NSF of Hebei Province(No.A2014205100)

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.Recently, it has been revealed that tensors are natural representations of multi- dimensional 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.

关 键 词：张量特征值 张量分解 图像处理 视频分析 

分 类 号：O151.23[理学—数学]