泛延拓矩阵的Schur分解及其应用  

Schur factorization of universal extended matrix and its application

作　　者：何静 袁晖坪 HE Jing;YUAN Huiping(School of Software,Chongqing Finance and Economics College,Chongqing 401320,China)

机构地区：[1]重庆财经学院软件学院,重庆401320

出　　处：《陕西理工大学学报（自然科学版）》2024年第6期75-81,共7页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(11871122);重庆市教委科技项目(KJQN201800815)。

摘　　要：基于泛延拓矩阵分解在数学和图像处理等领域中应用的重要性,利用矩阵分解理论导出了泛延拓矩阵的Schur分解、Hermite阵分解、正交对角分解和广义逆的优化计算公式。结果表明,此法在不降低数值精度的情况下减少了计算量与存储量,简化了数字版权保护领域中基于泛延拓阵Schur分解的彩色图像盲水印算法。Based on the importance of universal extended matrix factorization in the fields of mathematics and image processing,the optimal calculation formula of the Schur factorization,Hermite factorization,orthogonal diagonal factorization and generalized inverse of universal extended matrix are derived by matrix decomposition theory.The results show that this method can reduce the computation and storage without reducing the numerical accuracy.It simplifies the color image blind watermarking algorithm based on universal extended matrix Schur factorization in digital copyright protection field.

关 键 词：泛延拓矩阵 SCHUR分解 广义逆 信号处理 数字水印 

分 类 号：TN911.7[电子电信—通信与信息系统] O151.21[电子电信—信息与通信工程]