一种基于野值剔除方法的稀疏重构算法

A SPARSE RECONSTRUCTION ALGORITHM BASED ON OUTLIER DELETION METHOD

在稀疏向量重构估计中,分段正交匹配追踪算法比较适合于大规模系统,而且具有严谨的渐近统计特性分析.但其对向量的估计速度以牺牲估计精度为代价.文章提出一种基于野值剔除方法的分段正交匹配追踪稀疏重构算法.首先,根据匹配滤波系数的混合概率分布,在算法每个运行阶段利用野值剔除法迭代估计其近似分布的参数.然后,结合估计的真阳性率来剔除假阳估计值并选择算法每个阶段的支撑集.该方法不仅使匹配滤波系数的分布参数得到更准确的估计,而且利用真阳性率较大地改善了稀疏重构的估计精度.数值仿真计算表明,在不显著增加计算复杂度的条件下,该算法可大幅度提高稀疏重构问题的估计精度.

Stagewise orthogonal matching pursuit is well suited to large-scale systems in sparse vector estimation,and has some attractive asymptotically statistical properties.However,the speed of vector estimation is at the cost of accuracy violation.In this paper,an algorithm of stagewise orthogonal matching pursuit based on the outlier deletion method is suggested.During one stage of the algorithm,according to the mixed probability distribution of coefficients of a matched filter,distribution parameters are estimated more accurately using an outlier deletion method.Then,a more accurate estimate of the support set is achieved on the basis of an estimated true positive rate,which results in a significant false positive rate reduction.This algorithm can not only more accurately estimate the parameters of distribution of matched filter coefficients,but also improve estimation accuracy for the sparse vector.Simulation results show that without significant increment in computation complexity,the proposed algorithm can greatly improve estimation accuracy for sparse reconstruction problems.