模型噪声中的稀疏恢复算法研究  

Research of Sparse Recovery Algorithm Based on Model Noise

作　　者：韩学兵[1] 张颢[2] 

机构地区：[1]空军空降兵学院,桂林541003 [2]清华大学电子工程系,北京100084

出　　处：《电子与信息学报》2012年第8期1813-1818,共6页Journal of Electronics & Information Technology

摘　　要：针对观测和传感矩阵都存在噪声扰动的欠定线性系统的稀疏恢复问题,该文基于FOCUSS(FOCal Underdetermined System Solver)算法提出了一种改进算法——SD(Synchronous Descending)-FOCUSS。文中由MAP(最大后验)估计方法推导出系统模型的的目标函数,应用松弛迭代算法对其进行优化从而找到近似最优的稀疏解。SD-FOCUSS算法可应用于MMV(多观测向量)模型。可证明SD-FOCUSS是收敛算法;最后用仿真实验展示了与其他算法相比时,新算法在准确性、稳定性等方面的优越性。For sparse recovery of underdetermined linear systems where noise perturbations exist in both the measurements and sensing matrix, based on FOCal Underdetermined System Solver （FOCUSS） algorithm, an improved algorithm, named Synchronous Descending （SD） -FOCUSS, is proposed. The objective function of system model is deduced through a Maximum A Posteriori （MAP） estimation; then approximate optimum sparse-solution can be found while optimizing objective function using iterative relaxation algorithm. Another breakthrough of SD-FOCUSS is that the new algorithm can be applied to Multiple Measurement Vector （MMV） models. The convergence of SD-FOCUSS algorithm can be established with mathematical proof. The simulation results illustrate advantages of the new algorithm on accuracy and stability compared with other algorithms.

关 键 词：信号处理 稀疏恢复 模型噪声 SD—FOCUSS 收敛性 

分 类 号：TN911.72[电子电信—通信与信息系统]