Regression methods are widely employed in face recognition applications. The vector-based norm regression model only represents the pixel by pixel correlation and exhibits poor performance with contiguous occlusion. In contrast, methods based on the nuclear norm describe the low-rank structural information, but it is difficult to achieve satisfactory performance when dealing with complex noise. To address this, a log-based non-convex relaxation regularized regression (log-NCRR) model for robust face recognition is proposed in this paper. We adopt the log-based matrix loss without additional parameters to characterize the low-rank part of error image. Considering sparsity, we design a log-based vector loss to describe the sparse part of the error matrix, which achieves a balance between the -norm and -norm. Additionally, a weighted non-convex relaxation of -norm is proposed to ensure the group sparsity of the regression coefficient. The optimization problem is optimized by ADMM, with the corresponding sub-problems easily solved by the generalized singular value shrinkage operator. Finally, experimental results on four public databases for various types of noise validate the effectiveness and robustness of log-NCRR in face recognition.

中文翻译：

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用于鲁棒人脸识别的基于对数的非凸松弛正则化回归

回归方法广泛应用于人脸识别应用中。基于向量的范数回归模型仅表示逐像素相关性，并且在连续遮挡时表现出较差的性能。相比之下，基于核范数的方法描述了低秩结构信息，但在处理复杂噪声时很难取得令人满意的性能。为了解决这个问题，本文提出了一种基于对数的非凸松弛正则回归（log-NCRR）模型，用于鲁棒人脸识别。我们采用基于对数的矩阵损失而不需要额外的参数来表征误差图像的低秩部分。考虑到稀疏性，我们设计了基于对数的向量损失来描述误差矩阵的稀疏部分，从而实现了-norm和-norm之间的平衡。此外，提出了-范数的加权非凸松弛来确保回归系数的组稀疏性。优化问题通过ADMM进行优化，相应的子问题可以通过广义奇异值收缩算子轻松求解。最后，在四个公共数据库上针对各种类型噪声的实验结果验证了 log-NCRR 在人脸识别中的有效性和鲁棒性。