结构扰动与粗差鲁棒的lp正交匹配追踪算法

针对压缩感知稀疏信号恢复,提出了一种对测量结构扰动和粗差同时鲁棒的l₁正交匹配追踪(structure perturbation and outlier robust l₁-orthogonal matching pursuit, l₁-SPOR-OMP)算法。该算法利用l₁范数对粗差的鲁棒性,分别约束信号和扰动的拟合误差,进而通过交替迭代使它们同时到达最小,从而同时实现对信号和扰动的有效鲁棒恢复;由于算法仅需求解支撑位置的有效扰动,因此极大地降低了算法的计算复杂度。此外,为了进一步提高算法的恢复效率,也提出了使用鲁棒OMP方法来估计有效扰动的l_1,2-SPOR-OMP算法。在证明了所提出算法收敛性的同时,分析了运算复杂度。数值仿真的结果验证了所提算法的有效性和优越性。

Structure perturbation and outlier robust lp-orthogonal matching pursuit

A robust algorithm for recovering the sparse signals with the structure perturbations and outliers, called the structure perturbation and outlier robust l₁-orthogonal matching pursuit (l₁-SPOR-OMP), is proposed. To make the algorithm be robust against outliers, the l₁ norm constraints are imposed on the fitting errors of the recovered signals and perturbations. It is shown that the signals and perturbations can effectively and robustly be recovered while thel₁ norms of the fitting errors are iteratively minimized alternatively. It is found that the effective perturbation vector with the same support as that of the signal can be employed to reduce the computation complexity of the proposed algorithm greatly. Furthermore, to improve the algorithm efficiency further, an algorithm with thel₁ norm constraint for the signals and l₂ one for the perturbations, named the l_1,2-SPOR-OMP, is also proposed, where a robust orthogonal matching pursuit (OMP) algorithm for thel₂ constraint term can be used more efficiently for estimating the effective perturbation. While the convergence of the proposed, algorithms is proved, their computational complexities are analytically given. The numerical simulation results verify the effectiveness of the proposed algorithms and their superiority over the state of art ones.