Abstract:

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 the l₁  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 the l₁  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 the l₂ 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.