广义奇异值分解的高阶图像低秩近似方法  

A Low-Rank Approximation Method for High-Order Images Based on Tensorial Singular Value Decomposition

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

机构地区：[1]中原工学院电子信息学院,郑州450007

出　　处：《电光与控制》2020年第12期53-57,共5页Electronics Optics & Control

基　　金：高端外国专家项目(GDW20186300351)。

摘　　要：针对合成孔径雷达图像易受外界环境干扰导致获取的图像信息准确度降低的问题,提出一种基于广义奇异值分解的高阶图像低秩近似方法。首先,在经典奇异值分解的基础上,利用邻域选取法将经典二维矩阵推广到广义高阶矩阵;其次,利用“t-product”模型将经典矩阵算法推广到广义矩阵的相关算法,得出广义奇异值分解的具体实现过程;最后,在广义奇异值分解和经典奇异值分解的条件下,通过实例分析并利用结构相似度和峰值信噪比比较其低秩近似性能。仿真实验验证了广义奇异值分解技术相比于经典奇异值分解,不仅充分考虑图像像素点之间的相互作用与空间结构,而且随着广义矩阵阶数的扩展,所获得的图像结构相似度越大,峰值信噪比越高,可将其应用于高阶图像的低秩近似、重构。To solve the problem that the accuracy of the acquired SAR image information is reduced due to the interference of external environmenta low-rank approximation method for high-order SAR images based on Tensorial Singular Value Decomposition(TSVD)is proposed.Firstlyon the basis of classical Singular Value Decomposition(SVD)the classical two-dimensional matrix is extended to the tensorial high-order matrix by using the neighborhood selection method.Secondlythe classical matrix algorithm is extended to the algorithm related to the tensorial matrix by using“t-product”modeland the specific implementation process of TSVD is obtained.Finallythe performance of low-rank approximation under the conditions of TSVD is compared with that of the classical SVD by using structural similarity and PSNR.The simulation results show thatcompared with the classical SVDthe TSVD fully considers the interaction and spatial structure between image pixelsand with the expansion of the order of the tensorial matrixthe higher the similarity of image structure and the higher the PSNR.The method can be applied to the low-rank approximation and reconstruction of high-order images.

关 键 词：合成孔径雷达图像 广义奇异值分解 奇异值分解 邻域选取法 “t-product”模型 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]