基于TSVD的高阶图像低秩近似新方法  

A NEW LOW RANK APPROXIMATION METHOD FOR HIGH-ORDER IMAGE BASED ON TSVD

作　　者：杨洁 魏平俊[1] 廖亮[1] Yang Jie;Wei Pingjun;Liao Liang(College of Electronics and Information,Zhongyuan University of Technology,Zhengzhou 450007,Henan,China)

机构地区：[1]中原工学院电子信息学院,河南郑州450007

出　　处：《计算机应用与软件》2020年第10期133-137,161,共6页Computer Applications and Software

基　　金：国家自然科学基金项目(U1404607)。

摘　　要：提出一种基于广义奇异值分解的高阶图像低秩近似新方法。在传统矩阵分析的基础上,介绍高阶广义矩阵的生成及定义,得出广义奇异值分解不仅适用于传统的实数矩阵,对高阶广义复数矩阵亦具有重要意义。实验在高阶图像低秩近似的基础上,提出两种改进方案,一是将传统的实数矩阵扩展成为高阶广义复数矩阵,二是在领域选取时,分析比较指数增长和线性增长方式的近似效果。数值实验验证了高阶广义复数矩阵具有更高的低秩近似效果,指数增长方式与线性增长方式相比具有明显的优越性。This paper proposes a new low rank approximation method for high-order image based on TSVD.On the basis of traditional matrix analysis,the generation and definition of high-order generalized matrix were introduced.It was concluded that generalized singular value decomposition was not only suitable for traditional real matrix,but also important for high-order generalized complex matrix.Based on the low-rank approximation of high-order images,two improved schemes were proposed.One was to extend the traditional real matrix to the high-order generalized complex matrix.The other was to compare with the approximation effects of exponential growth and linear growth in the field selection.The numerical experiments show that the higher-order generalized complex matrix has a higher approximation effect of low rank,and the exponential growth mode is superior to the linear growth mode.

关 键 词：高阶广义复数矩阵 广义奇异值分解 高阶图像低秩近似 领域选取 指数增长 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]