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.

大多数现有的基于回归的分类方法都可以通过\（\ ell _1 \）- norm或\（\ ell _2 \）来处理像素级噪声-规范，但忽略像素之间的结构信息。据我们所知，基于核范数的矩阵回归方法在解决图像噪声方面取得了巨大成功，但可能会导致不合理的回归和不正确的分类，尤其是当测试图像因较大的遮挡和严重的光照变化而严重损坏时，因为它们将损坏的测试图像直接用于重建过程，将不可避免地受到噪声的影响。为了克服这个限制，本文提出了一个鲁棒的混合范数约束回归模型来处理结构噪声破坏。更具体地说，将破坏的测试图像与其相应的恢复图像之间的误差的核规范用作表征低秩噪声结构的常规术语，由于恢复图像的噪声较小，因此利用Frobenius范数来描述恢复图像与重构图像之间的差异。然后，我们采用乘数的交替方向方法来有效地解决我们提出的方法。此外，提供了理论上的收敛性证明和对计算复杂度的详细分析，以评估我们的算法。最终，在五个著名的人脸数据库上进行的广泛实验表明，所提出的方法优于某些基于回归的最新方法，该方法主要用于解决由遮挡和照明变化引起的噪声。我们采用乘数的交替方向方法来有效地解决我们提出的方法。此外，提供了理论上的收敛性证明和对计算复杂度的详细分析，以评估我们的算法。最终，在五个著名的人脸数据库上进行的广泛实验表明，所提出的方法优于某些基于回归的最新方法，该方法主要用于解决由遮挡和照明变化引起的噪声。我们采用乘数的交替方向方法来有效地解决我们提出的方法。此外，提供了理论上的收敛性证明和对计算复杂度的详细分析，以评估我们的算法。最终，在五个著名的人脸数据库上进行的广泛实验表明，所提出的方法优于某些基于回归的最新方法，该方法主要用于解决由遮挡和照明变化引起的噪声。