低秩稀疏矩阵分解在视频监控中的应用

发布时间：2018-10-09 11:28

【摘要】：近十年来,随着摄像机的普及和网络技术的高速发展,我们面临的视频监控数据也出现井喷式地增加,给我们的数据分析带来了一系列的问题.例如：在大数据时代,如何存储大规模的视频数据?如何快速寻找到异常片段?如何根据已知信息,在视频库中寻找相关的视频?压缩感知的出现解决了这些问题,本文利用压缩感知的相关理论,主要研究低秩稀疏矩阵分解在视频监控中的应用.基于凸松弛理论,假设低秩矩阵的秩为1,那么低秩稀疏矩阵分解问题就会转化为秩-1稀疏矩阵分解问题.针对该模型,提出了修正的变权重置L1算法.与传统的交替方向法相比,大大提高了算法的精度.随后,将秩-1稀疏矩阵分解的思想应用到磁共振成像中,提出修正的交替方向法.通过数值实验表明,该算法更易于发现病变的区域,为治疗带来了极大的好处.基于非凸松弛理论,针对传统的低秩稀疏矩阵分解问题,提出用S1/2范数代替秩、用L1/2范数代替L1范数的想法,得到非凸、非光滑、非Lispchitz的A1/2-L1/2模型.由于每个子问题都有显示解,能够给出快速的迭代半阈值算法.应用不动点方法,给出相应的收敛性结果.最后,对文章进行总结.
[Abstract]:In the past decade, with the popularization of video cameras and the rapid development of network technology, the video surveillance data we are faced with has also increased by blowout, which has brought a series of problems to our data analysis. For example: in big data's time, how to store large-scale video data? How to find exception fragments quickly? How to find the relevant video in the video library based on the known information? The emergence of compressed sensing solves these problems. This paper mainly studies the application of low rank sparse matrix decomposition in video surveillance by using the theory of compressed sensing. Based on convex relaxation theory, assuming that the rank of low rank matrix is 1, the problem of low rank sparse matrix decomposition will be transformed into rank 1 sparse matrix factorization problem. For this model, a modified L1 algorithm with variable weights is proposed. Compared with the traditional alternating direction method, the accuracy of the algorithm is greatly improved. Then, the rank-1 sparse matrix decomposition is applied to magnetic resonance imaging, and a modified alternating direction method is proposed. Numerical experiments show that the algorithm is easier to find the lesion area and brings great benefits to the treatment. Based on the theory of non-convex relaxation, the idea of replacing rank with S _ 1 / 2 norm and L _ 1 / 2 norm instead of L _ 1 norm is proposed to solve the traditional low-rank sparse matrix decomposition problem. A non-convex, non-smooth and non-Lispchitz A1/2-L1/2 model is obtained. Since each subproblem has a display solution, a fast iterative semi-threshold algorithm can be given. By using the fixed point method, the corresponding convergence results are given. Finally, the article is summarized.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O151.21;TN948.6

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