A Robust Orthogonal Matching Pursuit Based on L1 Norm

Abstract

Compressed sensing theory is a new sampling theory in recent years. Orthogonal matching pursuit(OMP) algorithm is one of the widely used reconstruction methods. For the problem of poor quality in OMP when there are outliers in the measurement vector, the OMP algorithm is improved by combining the characteristics of L 1 norm, and a robust Orthogonal Matching Pursuit based on L 1 Norm(L 1 OMP) is proposed. Compared with the traditional OMP algorithm, the L 1 OMP algorithm is robust to outliers. This is because the traditional OMP algorithm uses the L 2 norm to estimate the sparse signal, and the L 2 norm is extremely sensitive to the outliers. In contrast, the robustness of the L 1 norm is good. In this paper, the L 1 OMP algorithm and the data preprocessing OMP algorithm are used to simulate the signal reconstruction. The simulation results show that the L 1 OMP algorithm can accurately reconstruct the signal when there is an outlier in the measurement vector.