鲁棒性在线子空间辨识与跟踪的关键问题研究

The major research of this proposal is to introduce a fast online algorithm which can robustly identify and track the low-rank subspace from highly incomplete high-dimensional data which are also corrupted by sparse outliers. From the algorithmic aspect, this proposal intends to study the optimization framework of Grassmannian manifold, and investigate the L-1 norm least absolute regression model from partial observed data, which is aiming for leveraging the corruption by sparse outliers. This proposal mainly focuses on regarding the augmented Lagrangian of the least absolute regression model as the subspace loss function and intends to incorporate this loss function into the Grassmannian stochastic gradient descent framework. From the theoretical aspect, this proposal will give a rigorous analysis that given the corruption fraction of uniformly distributed sparse outliers, how much the low bound of the missing data ratio is. And also the proof of the global optimum convergence of this proposed online robust subspace identification algorithm will be given. From the application aspect, this proposal intends to apply the proposed theory and algorithm to the task of real-time separating moving objects from background in video surveillance. And This proposal will also dig into the novel approach for online robust face images alignment based on the proposed online robust subspace identification algorithm in this proposal. Two demo projects of real-time background and foreground separation and online face images alignment will be developed for investigating the efficiency and effectiveness of the core theory and algorithm studied in this proposal.

在数据高度缺失、甚至数据受异常噪声污染的苛刻条件下，快速从高维数据中辨识出低秩子空间并进行子空间跟踪，是本项目的主要研究内容。本项目将研究格拉斯曼流形的随机梯度下降最优化理论，研究在数据缺失情况下1-范数最优化模型的增广拉格朗日形式，通过选择合适的子空间辨识问题代价损失函数，由此进行随机梯度下降算法的推导及收敛性证明。本项目将从视频监控中实时背景/前景分离，人脸序列图像的在线对准两方面，研究鲁棒性子空间在线辨识与跟踪在计算机视觉问题中的应用，并开发出示范系统验证算法的有效性与实时性。

本课题主要研究了鲁棒性在线子空间辨识与跟踪问题。课题的在五个方面进行了深入的研究：1）在线鲁棒性迭代子空间学习算法的研究，我们提出了t-GRASTA算法，通过迭代式子空间学习，该算法能够完全在线的恢复出低维子空间和估计出图像的几何形变参数；2）基于交替方向Grassmannian最优化的在线鲁棒性视频背景建模，我们提出了基于Grassmannian优化方法的鲁棒性子空间学习方法，并将其应用于视频的背景建模，即使视频出现抖动等退化情况；3）压缩感知下的子空间在线辨识与信号恢复问题的研究，我们提出一种固定子空间的稀疏信号重构算法，能够以更低的采样率恢复稀疏信号；4）混杂异常数据的在线子空间辨识问题，我们提出一种快速算法GASG21，能够在大量异常数据污染的条件下，以线性的收敛速度恢复低维子空间并进行子空间聚类；5）面向视觉大数据的若干应用，我们研究了大数据平台Hadoop和Spark下图像分类和视频中人的行为识别相关算法。