矩阵广义逆硬阈值追踪算法与稀疏恢复问题  

MATRIX PSEUDOINVERSE HARD THRESHOLDING PURSUIT AND SPARSE RECOVERY PROBLEM

作　　者：施章磊 李维国 

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《计算数学》2017年第2期189-199,共11页Mathematica Numerica Sinica

基　　金：中央高校基本科研业务费(15CX05051A;15CX02055A;16CX02011A);山东省自然科学基金(ZR2014AQ004);山东省优秀中青年科学家科研奖励基金(2014BSE28027)资助项目

摘　　要：本文通过引入支撑集捕获基数及MP广义逆,提出了一种用于稀疏恢复问题的矩阵广义逆硬阈值追踪算法,并在观测误差存在的情况下给出了算法在约束等距条件(RIP)下的收敛性.数值实验表明,算法不仅极大地减少了收敛所需迭代次数,且观测误差存在的情况下稀疏恢复是强健的.In this paper, based on pseudoinverse and a newly introduced capture cardinality of support set, the new algorithm, Matrix Pseudoinverse Hard Thresholding Pursuit, is proposed to find the sparse solutions of underdetermined linear systems.The convergence is established under restricted isometry property （RIP） condition in the situation where observation error exist. Numerical experiments show that the proposed algorithm not only significantly reduce the iteration number required for convergence, but also can robustly recover the original signal when measurements contain errors.

关 键 词：压缩感知 稀疏恢复 硬阈值追踪 广义逆 

分 类 号：O151.21[理学—数学]