Abstract: Due to the self-expressive property of data, the samples from same class have similar representations over a given dictionary, which means the representations of all samples possess block-diagonal structure. But in view of the existence of various corruptions in face images, the sample’s subspace structure may be destroyed. In order to handle this problem, many low-rank representation based methods are proposed to recovery clear components of data, but only low-rank constraint can not transform the original training samples to ideal low-rank subspace perfectly. A Robust Structured Low-Rank Recovery algorithm（RSLRR） is proposed. RSLRR utilizes an ideal label matrix to promotethe low-rank representation tend to a block-diagonal structure which can excavate more potential structural information. Meanwhile, in order to alleviate the structural information loss caused by above strict label pursuing, another relax regularization term are applied to weaken the negative influence of off-block-diagonal coefficients. Afterwards, a discriminative and structured dictionary can be obtained by RSLRR algorithm, and then a low-rank projection matrix is computed to project all test samples into its corresponding low-rank subspaces efficiently. Experimental results on AR and CMU PIE databases demonstrate the effectiveness and robustness of the proposed RSLRR algorithm.

Key words: face recognition, block-diagonal structure, low-rank recovery, subspace projection, feature extraction

摘要： 由于数据本身的自表示特性，当给定一个字典时，同类样本理论上具有相似的线性表示，所以所有样本的表示矩阵具有块对角结构。但在由于样本中存在的各种污损，数据子空间结构可能会被破坏。为了解决这一问题，很多基于低秩表示的恢复算法相继提出，但是仅有对表示的低秩约束并不能很好地将原始训练样本转化到理想的低秩子空间。因此，提出了一个鲁棒的结构化低秩恢复算法（Robust Structured Low-Rank Recovery，RSLRR）。RSLRR利用理想的标签矩约束阵促进低秩表示趋近于块对角结构，以此挖掘更多的潜在结构信息。同时，为了减少严格的趋近0-1标签矩阵造成的结构信息损失，RSLRR增加了一个正则化项用来减弱非块对角系数的负面影响。通过RSLRR算法可以得到一个判别的结构化字典，并可计算出一个低秩投影矩阵将所有测试样本有效的投影到其相应的低秩子空间。在AR和CMU PIE数据库上的实验结果验证了RSLRR算法的有效性和鲁棒性。

关键词: 人脸识别, 块对角结构, 低秩恢复, 子空间投影, 特征提取