Robust sparse representation based on fitting error decomposition

Abstract

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.