Low-rank sparse regression models have been widely adopted in face recognition due to their robustness against occlusion and illumination variations. However, existing methods often suffer from insufficient feature representation and limited modeling of structured corruption across samples. To address these issues, this paper proposes a Hybrid second-order gradient Histogram based Global Low-Rank Sparse Regression (H2H-GLRSR) model. First, we propose the Histogram of Oriented Hessian (HOH) to capture second-order geometric characteristics such as curvature and ridge patterns. By fusing HOH and first-order gradient histograms, we construct a unified local descriptor, termed the Hybrid second-order gradient Histogram (H2H), which enhances structural discriminability under challenging conditions. Subsequently, the H2H features are incorporated into an extended version of the Sparse Regularized Nuclear Norm based Matrix Regression (SR\_NMR) model, where a global low-rank constraint is imposed on the residual matrix to exploit cross-sample correlations in structured noise. The resulting H2H-GLRSR model achieves superior discrimination and robustness. Experimental results on benchmark datasets demonstrate that the proposed method significantly outperforms state-of-the-art regression-based classifiers in both recognition accuracy and computational efficiency.

翻译：低秩稀疏回归模型因其对遮挡和光照变化的鲁棒性，在人脸识别领域得到广泛应用。然而，现有方法常面临特征表示不足以及对样本间结构化噪声建模有限的问题。为解决这些挑战，本文提出了一种基于混合二阶梯度直方图的全局低秩稀疏回归模型。首先，我们提出方向Hessian直方图以捕捉曲率和脊线模式等二阶几何特征。通过融合HOH与一阶梯度直方图，构建了统一的局部描述符——混合二阶梯度直方图，该描述符增强了复杂条件下的结构判别能力。随后，将H2H特征整合至基于稀疏正则化核范数的矩阵回归模型的扩展版本中，通过对残差矩阵施加全局低秩约束以利用结构化噪声中的跨样本相关性。所提出的H2H-GLRSR模型实现了卓越的判别性与鲁棒性。在基准数据集上的实验结果表明，该方法在识别精度与计算效率方面均显著优于当前最先进的基于回归的分类器。