Research On Robust Principle Component Analysis And Its Applications

Recovering efficiently the low-rank structure of observed data which is corrupted by gross errors and outliers has been widely applied in the fields of computer vision,such as pattern recognition,video/signal processing and industrial inspection.With the development of its theory,robust principle component analysis(RPCA)has got more and more attention,which is considered as the extension of principle component analysis.It can not only efficiently recover and analyze the low-rank structure of observed data,but also acquire the sparse component of observed data.In this thesis,we study the theory and actual applications of the RPCA.In addition,we propose the corresponding algorithms based on the RPCA in cases of real-world applications.(1)An improved method is proposed to.detect contiguous outliers,which is based on the low-rank representation(DECELOR).The DECELOR algorithm is the extension of RPCA,which incorporates prior knowledge on the spatial distribution of foreground moving objects.However,DECELOR still takes nuclear norm to relax the rank of data matrix,which is not well in reflecting the correlation between background images in video frames.To solve this problem,we introduce a concave function into the DECELOR.In addition,we utilize a prior target rank information about the background component in observed videos.So,in this thesis,concave function and partial nuclear norm are employed to take place of original nuclear norm in iterations.Experiments demonstrate that the improved algorithm outperforms the RPCA-based moving detection algorithms.(2)Defect inspection for IC solder joints is a long-standing task.This thesis proposes a novel IC solder joint inspection method based on the idea of RPCA,which formulates IC solder joint inspection as an optimization problem.In particular,we model an IC solder joint image as observed data corrupted by gross errors.According to the RPCA theory,the IC solder joint images can be approximately decomposed into a low-rank component and an error component.In this paper,an appearance model of qualified IC solder joints is defined for IC solder joint inspection based on RPCA.Then,a defect score is defined based on the appearance model and used to evaluate the quality of IC solder joints.Meanwhile,location prior knowledge related to human perception is incorporated in the defect score to further evaluate the defects of IC solder joints.Finally,a simply discrimination scheme is proposed to inspect IC solder joints.Experimental results indicate that the proposed method is superior to the existing methods in inspection performance.