Robust mixed-norm constrained regression with application to face recognitions

Abstract

Most existing regression-based classification methods cope with pixelwise noise via $$\ell _1$$ -norm or $$\ell _2$$ -norm, but neglect the structural information between pixels. To the best of our knowledge, nuclear norm-based matrix regression approaches have achieved great success for addressing imagewise noise, but may result in unreasonable regression and incorrect classification, especially when test images are extremely corrupted by larger occlusions and severe illumination variations, since they apply the corrupted test images to reconstruction process directly, and the influence of noise will be unavoidable. To overcome this limitation, this paper presents a robust mixed-norm constrained regression model to deal with the structural noise corruption. To be more specific, nuclear norm of the error between corrupted test image and its corresponding recovered image is exploited as a regular term for characterizing the low rank noise structure, and Frobenius norm is utilized to depict the difference between the recovered image and restructured image on account of the less noise of recovered image. Then, we adopt the alternating direction method of multipliers to settle our proposed approaches efficiently. Furthermore, the theoretical convergence proof and detailed analysis of computational complexity are provided to assess our algorithms. Eventually, extensive experiments on five well-known face databases have manifested that the proposed methods outperform some state-of-the-art regression-based approaches for primarily addressing noise caused by occlusion and illumination changes.