Based On A Robust Principal Component Analysis And Its Application In Target Detection Research

Principal Component Analysis is arguably the most widely used statistical tool for data anlysis and dimensionality reduction today. Currently, it has been widely used in fault diagnosis, data compression, signal processing and pattern recognition. However, in many applications, traditional principal component analysis is very brittle, and its brittleness with respect to gossly corrupted observations often puts its validity in jeoardy, a single grossly corrupted entry could make the final results far from the original space. Unfortunately, gross errors are now ubiquitous in mordern applications such as image processing, medical images and video survillance, where some measurements may be arbitratily corrupted or simply irrelevant to the low-dimensional structure due to occlusions, illumination or noise. This problem may imact the application of preinciple component analysis algorithms in the pratical systems, and our job is to reaserch how to recover each component individually.We first introduce the basic theory of principal component analysis, describes the implementation process of principal component analysis. Then on the basic existing work,establish a robust principal component analysis method:suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component.On the theory aspect: we prove under some suitable assumption, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit,among all feasible decompositions, simply minimize a weighter combination of the nuclear norm and of the l1, norm. This suggests the possibility of a principled approach to robust principle components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted.On application aspect:we discuss the algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of moving objects in a cluttered background, and comare with the other mothod too.