Robust face recognition based on the wing loss and the $\ell_1$ regularization

In recent years, sparse sampling techniques based on regression analysis have witnessed extensive applications in face recognition research. Presently, numerous sparse sampling models based on regression analysis have been explored by various researchers. Nevertheless, the recognition rates of the majority of these models would be significantly decreased when confronted with highly occluded and highly damaged face images. In this paper, a new wing-constrained sparse coding model(WCSC) and its weighted version(WWCSC) are introduced, so as to deal with the face recognition problem in complex circumstances, where the alternating direction method of multipliers (ADMM) algorithm is employed to solve the corresponding minimization problems. In addition, performances of the proposed method are examined based on the four well-known facial databases, namely the ORL facial database, the Yale facial database, the AR facial database and the FERET facial database. Also, compared to the other methods in the literatures, the WWCSC has a very high recognition rate even in complex situations where face images have high occlusion or high damage, which illustrates the robustness of the WWCSC method in facial recognition.