2种低秩矩阵恢复优化模型的误差估计定理  

Error estimation theorems of two low rank matrix restoration optimization models

作　　者：郑珂 宋儒瑛[1] ZHENG Ke;SONG Ru-ying(Department of mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《云南民族大学学报（自然科学版）》2024年第3期396-400,410,共6页Journal of Yunnan Minzu University:Natural Sciences Edition

摘　　要：近年来低秩矩阵恢复问题逐渐引起人们的关注,类似于向量稀疏恢复的充分条件是需要测量矩阵满足限制等距性质,低秩矩阵恢复的充分条件是需要一个线性映射满足限制等距性质.低秩矩阵恢复时所需的模型大致分为有噪和无噪两种恢复模型,恢复出来的结果需要不同的限制等距常数界去保证.文章证明了这2种优化模型的误差界估计定理,并得出了2种不同的限制等距常数界.In recent years,the problem of low rank matrix restoration has gradually attracted people's attention.Sim⁃ilar to vector sparse restoration,the sufficient condition is that the measurement matrix needs to meet the Restricted isometric property,and the sufficient condition of low rank matrix restoration is that a linear mapping needs to meet the Restricted isometric property.The restoration of low rank matrix is divided into two restoration models with noise and no noise.The restored results need different restricted isometric constant bounds to ensure.In this paper,the er⁃ror bound estimation theorems of the two optimization models are proved,and two different restricted isometric con⁃stant bounds are obtained.

关 键 词：线性映射的限制等距性质 低秩矩阵恢复 压缩感知 FROBENIUS范数 

分 类 号：O178[理学—数学]