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arXiv 1007.3753cs.CVcs.NAmath.NA

用于鲁棒人脸识别的快速L1最小化算法

Fast L1-Minimization Algorithms For Robust Face Recognition

University of California, Berkeley(加州大学伯克利分校);University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校);IBM Research(IBM研究院);Microsoft Research Asia(微软亚洲研究院)

Allen Y. Yang, Zihan Zhou, Arvind Ganesh, S. Shankar Sastry, Yi Ma

AI总结:

针对鲁棒人脸识别中的稀疏表示分类框架,提出基于增广拉格朗日方法的快速L1最小化解法,解决了传统算法在大规模应用中的可扩展性问题。

摘要:

L1最小化是指在欠定线性系统b=Ax中寻找最小L1范数解。根据压缩感知理论中的某些条件,最小L1范数解也是最稀疏的解。本文研究其算法的速度和可扩展性。特别地,我们关注鲁棒人脸识别中基于稀疏性的分类框架的数值实现,其中通过稀疏表示从可能被光照、面部伪装和姿态变化破坏的高维人脸图像中恢复人类身份。尽管底层数值问题是线性规划,但传统算法在大规模应用中可扩展性差。我们研究了一种基于经典凸优化框架——增广拉格朗日方法(ALM)的新解法。新的凸求解器为实时、时间关键的应用(如人脸识别)提供了可行的解决方案。我们进行了大量实验,验证并比较了ALM算法与几种流行的L1最小化解法(包括内点法、Homotopy、FISTA、SESOP-PCD、近似消息传递(AMP)和TFOCS)的性能。为便于同行评估,所有算法的代码均已公开。

英文摘要:

L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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