基于l₁-al₂最小化的部分支集已知的信号重建  

Signal Reconstruction with Known Partial Support Based on l1-al2 Minimization

作　　者：武思琪 宋儒瑛[1] 

机构地区：[1]太原师范学院数学系,山西 晋中

出　　处：《应用数学进展》2022年第8期6015-6028,共14页Advances in Applied Mathematics

摘　　要：压缩感知中测量矩阵的限制等距性在一定条件下可以确保重建稀疏信号。文章在l1-al2(0 < a≤1)最小化问题模型下,根据已知信号的先验支撑信息,利用测量矩阵的限制等距性,研究了三种噪声(高斯噪声、脉冲噪声、均匀噪声)情形下信号恢复的充分条件。这些条件直观地揭示了测量矩阵的限制等距性和信号恢复之间的密切关系。The restricted isometry property of the measurement matrix in compressed sensing can ensure the reconstruction of sparse signals under certain conditions. In this paper, the sufficient conditions for signal recovery under three kinds of noise (Gaussian noise, impulse noise and uniform noise) are studied according to the known prior support information of the signal and the restricted isometry property of the measurement matrix under l1-al2(0

关 键 词：压缩感知 信号恢复 l₁-al₂最小化 限制等距性 部分支集已知 

分 类 号：O151.21[理学—数学]