Abstract Strict ‘0-1’ block-diagonal structure has been widely used for learning structured representation in face recognition problems. However, it is questionable and unreasonable to assume the within-class representations are the same. To circumvent this problem, in this paper, we propose a slack block-diagonal (SBD) structure for representation where the target structure matrix is dynamically updated, yet its blockdiagonal nature is preserved. Furthermore, in order to depict the noise in face images more precisely, we propose a robust dictionary learning algorithm based on mixed-noise model by utilizing the above SBD structure (SBD2L). SBD2L considers that there exists two forms of noise in data which are drawn from Laplacian and Gaussion distribution, respectively. Moreover, SBD2L introduces a low-rank constraint on the representation matrix to enhance the dictionary’s robustness to noise. Extensive experiments on four benchmark databases show that the proposed SBD2L can achieve better classification results than several state-of-the-art dictionary learning methods.

中文翻译：

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用于人脸识别的具有松弛块对角线结构的噪声鲁棒字典学习

摘要 严格的“0-1”块对角结构已被广泛用于学习人脸识别问题中的结构化表示。然而，假设类内表示相同是有问题和不合理的。为了规避这个问题，在本文中，我们提出了一种松弛块对角（SBD）结构来表示，其中目标结构矩阵是动态更新的，但其块对角性质被保留。此外，为了更精确地描述人脸图像中的噪声，我们利用上述 SBD 结构（SBD2L）提出了一种基于混合噪声模型的鲁棒字典学习算法。SBD2L 认为数据中存在两种形式的噪声，分别来自拉普拉斯分布和高斯分布。而且，SBD2L 在表示矩阵上引入了低秩约束，以增强字典对噪声的鲁棒性。在四个基准数据库上的大量实验表明，与几种最先进的字典学习方法相比，所提出的 SBD2L 可以获得更好的分类结果。