文献类型：期刊文献

英文题名：Robust compressed sensing with bounded and structured uncertainties

作者：Qing, Xiangyun[1,2];Hu, Guosheng[3];Wang, Xingyu[1,2]

机构：[1]Minist Educ, Key Lab Adv Control & Optimizat Chem Proc, Shanghai, Peoples R China;[2]E China Univ Sci & Technol, Dept Automat, Shanghai 200237, Peoples R China;[3]Univ Surrey, Ctr Vis Speech & Signal Proc, Guildford GU2 5XH, Surrey, England

年份：2014

卷号：8

期号：7

起止页码：783

外文期刊名：IET SIGNAL PROCESSING

收录：;EI(收录号：20143900070300);WOS:【SCI-EXPANDED(收录号:WOS:000342221800009)】；

语种：英文

外文关键词：compressed sensing; convex programming; perturbation techniques; matrix multiplication; least mean squares methods; estimation theory; minimisation; bounded uncertainty; structured uncertainty; robust compressed sensing problem; structured perturbation; bounded perturbation; sensing matrix; alternating direction method of multipliers; ADMM algorithm; robust signal recovery; convex optimisation problem; standard robust regularised least square problem; recovery error reduction; robust support set estimation; signal magnitude recovery; worst cast data error minimisation

摘要：The robust compressed sensing problem subject to a bounded and structured perturbation in the sensing matrix is solved in two steps. The alternating direction method of multipliers (ADMM) is first applied to obtain a robust support set. Unlike the existing robust signal recovery solutions, the proposed optimisation problem is convex. The ADMM algorithm that every subproblem has a global minimum is employed to solve the optimisation problem. Then, the standard robust regularised least-squares problem restrained to the support is solved to reduce the recovery error. The numerical tests show that the proposed approach provides a robust estimation of support set, although it is conservative to recover signal magnitudes as a result of minimising the worst-cast data error across all bounded perturbations.