Robust Recovery of Corrupted Image Data Based on $L_{1-2}$ Metric

For removing noises and recovering intrinsic structure from corrupted image data, a classic modeling approach is based on sparsity assumption. In traditionally, the sparsity is measured by L₁-norm. However, L₁-norm often leads to bias estimation and the solution is not as accurate as desired. To address this problem, this paper presents a new but effective data recovery model based on the L_1-2 metric, enabling the robust recovery of corrupted data. The L_1-2 metric is a non-convex approximation to L₀-norm and defined by the difference of L₁- and L₂-norms. The significant characteristic of our model is measuring both recovery data and error by the L_1-2 metric. Our model allows for efficient optimization by two steps. Extensive experimental results show significant improvement compared with state-of-the-art algorithms.