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 $L_{1}$ -norm. However, $L_{1}$ -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 $L_{0}$ -norm and defined by the difference of $L_{1}$ - and $L_{2}$ -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.