A robust mixed error coding method based on nonconvex sparse representation

Linear representation based methods have been extensively applied in image recognition, especially for those with noise, illumination changes, and occlusions. However, most existing methods assume a specific distribution for image noise estimation, which is intractable to handle complex variations. Besides, they usually use convex norm to describe the noise sparse and low -rank property, and it is a biased approximation. To address these problems, we propose a novel nonconvex regularized robust mixed error coding (NRRM) method, which uses mixed norms from both 1D and 2D perspectives to model the complex image noise without convex relaxation. In specific, we use weighted e2-norm based robust coding to characterize the sparse noise in images, and weighted matrix nuclear norm to characterize the low-rank noise. Compared with traditional regression approaches, our method can more fine-grained and accurate to capture noise and alleviate its negative influence for robust recognition. Besides, we constrain the representation component in a group-wise manner to weigh the roles of different classes. The NRRM model is solved efficiently by adopting an alternating direction method of multipliers (ADMM) algorithm. Comprehensive experiments on some benchmark face image databases validate the superiority of NRRM over several state-of-the-art linear representation based methods.