Institute of Automation, Chinese Academy of Sciences, Beijing.
Sun Yat-sen University, Guangzhou.
IEEE Trans Pattern Anal Mach Intell. 2014 Feb;36(2):261-75. doi: 10.1109/TPAMI.2013.102.
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.
鲁棒稀疏表示在解决计算机视觉中的挑战性问题，如生物识别和视觉监控方面显示出了巨大的潜力。尽管已经提出了几种鲁棒稀疏模型，并取得了有希望的结果，但它们要么用于纠错，要么用于错误检测，学习一个系统地统一这两个方面并探索它们之间关系的通用框架仍然是一个开放的问题。在本文中，我们开发了一个半二次 (HQ) 框架来解决鲁棒稀疏表示问题。通过定义不同种类的半二次函数，所提出的 HQ 框架适用于执行纠错和错误检测。更具体地，通过使用 HQ 的加性形式，我们提出了一种通过从噪声和异常值引起的错误中迭代恢复损坏的数据来进行 ℓ1 正则化纠错的方法；通过使用 HQ 的乘性形式，我们提出了一种通过从无错误的数据中迭代学习来进行 ℓ1 正则化错误检测的方法。我们还表明，通过软阈值函数求解的 ℓ1 正则化与 Huber M 估计器具有对偶关系，这从理论上保证了鲁棒稀疏表示在 M 估计方面的性能。在严重遮挡和损坏下的鲁棒人脸识别实验验证了我们的框架和发现。
