Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

基于l^(1/2)-TV正则化RPCA的运动目标检测

针对复杂环境下背景干扰导致运动目标检测精度下降的问题,提出了一种基于l^(1/2)-TV正则化RPCA的运动目标检测方法。方法利用核范数来描述背景的低秩特性,采用l^(1/2)范数描述更稀疏的运动目标,以抑制运动目标中的背景干扰。同时结合TV正则化约束运动目标的空间连续性,使运动目标更加完整。利用Frobenius范数检测背景干扰。采用交替方向最小化策略扩展的增广拉格朗日乘子法求解所提出的约束最小化问题。实验结果表明,所提方法能有效去除背景干扰,提高运动目标的检测精度、改善视觉效果。

变转速下L_(1,1,2)范数与张量核范数联合约束的TRPCA滚动轴承故障特征提取方法

滚动轴承作为旋转机械设备的重要部件之一,其工作状态直接影响旋转设备的运行安全,因此其故障特征的有效提取对于保障机械设备正常运行具有重要的意义。实际应用中滚动轴承通常以变化的速度运行,并且单一传感器采集的轴承的非平稳信号往往被严重的背景噪声覆盖,使得故障特征的提取非常困难。为了解决这一问题,提出一种变转速下L_(1,1,2)范数与张量核范数联合约束的张量主成分分析(tensor robust principal component analysis,TRPCA)滚动轴承故障特征提取方法。首先,使用时频表示(time-frequency representation,TFR)作为正向切片构建张量,分别探讨滚动轴承时变故障特征在张量域中的管稀疏性和背景噪声在张量域中的低管秩性。进而使用L_(1,1,2)范数与张量核范数联合约束的TRPCA对故障特征张量进行提取,得到管稀疏的故障特征张量。最后将提取的故障特征张量在通道索引中进行融合,得到能够有效表征故障特征的时频表示。仿真和试验分析验证了该方法在轴承故障特征提取中的有效性。

基于RPCA的红外与可见光图像融合

图像融合中,多数边缘保持滤波器在优化过程中会损坏细节和纹理信息,并且噪声也会严重影响融合结果,使得融合结果之间出现边界模糊和细节丢失问题。提出了一种基于RPCA(Robus principal compo-nent association)算法的红外光和可见光图像融合方法,可有效提高图象清晰度和视觉信息的保真度。首先,利用鲁棒主成分分析(RPCA)分解源图像为低秩部分和稀疏部分,并运用相对全变分和平均能量法对两者进行处理,最后通过NSCT逆变换获得融合图像。实验结果表明,与其他方法相比,该方法所得融合图像的平均梯度、空间频率、边缘强度、互信息量均有提升,提升量级分别为10.6%到72.6%、15%到60.2%、9.7%到69.6%,22.7%到229.7%。

Multivariate Statistical Process Monitoring Using Robust Nonlinear Principal Component Analysis

The principal component analysis （PCA） algorithm is widely applied in a diverse range of fields for performance assessment, fault detection, and diagnosis. However, in the presence of noise and gross errors, the nonlinear PCA （NLPCA） using autoassociative bottle-neck neural networks is so sensitive that the obtained model differs significantly from the underlying system. In this paper, a robust version of NLPCA is introduced by replacing the generally used error criterion mean squared error with a mean log squared error. This is followed by a concise analysis of the corresponding training method. A novel multivariate statistical process monitoring （MSPM） scheme incorporating the proposed robust NLPCA technique is then investigated and its efficiency is assessed through application to an industrial fluidized catalytic cracking plant. The results demonstrate that, compared with NLPCA, the proposed approach can effectively reduce the number of false alarms and is, hence, expected to better monitor real-world processes.

Robust Recommendation Algorithm Based on Kernel Principal Component Analysis and Fuzzy C-means Clustering

The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy c-means clustering. Firstly, we use kernel principal component analysis method to reduce the dimensionality of the original rating matrix, which can extract the effective features of users and items. Then, according to the dimension-reduced rating matrix and the high correlation characteristic between attack profiles, we use fuzzy c-means clustering method to cluster user profiles, which can realize the effective separation of genuine profiles and attack profiles. Finally, we construct an indicator function based on the attack detection results to decrease the influence of attack profiles on the recommendation, and incorporate it into the matrix factorization technology to design the corresponding robust recommendation algorithm. Experiment results indicate that the proposed algorithm is superior to the existing methods in both recommendation accuracy and robustness.

A new image processing method for discriminating internal layers from radio echo sounding data of ice sheets via a combined robust principal component analysis and total variation approach

Discriminating internal layers by radio echo sounding is important in analyzing the thickness and ice deposits in the Antarctic ice sheet.The signal processing method of synthesis aperture radar(SAR)has been widely used for improving the signal to noise ratio(SNR)and discriminating internal layers by radio echo sounding data of ice sheets.This method is not efficient when we use edge detection operators to obtain accurate information of the layers,especially the ice-bed interface.This paper presents a new image processing method via a combined robust principal component analysis-total variation(RPCA-TV)approach for discriminating internal layers of ice sheets by radio echo sounding data.The RPCA-based method is adopted to project the high-dimensional observations to low-dimensional subspace structure to accelerate the operation of the TV-based method,which is used to discriminate the internal layers.The efficiency of the presented method has been tested on simulation data and the dataset of the Institute of Electronics,Chinese Academy of Sciences,collected during CHINARE 28.The results show that the new method is more efficient than the previous method in discriminating internal layers of ice sheets by radio echo sounding data.

Robust Principal Component Analysis via Truncated Nuclear Norm Minimization

Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.

Applications of gauge duality in robust principal component analysis and semidefinite programming

Gauge duality theory was originated by Freund(1987), and was recently further investigated by Friedlander et al.(2014). When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach,a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming(SDP) problems with promising numerical results by Friedlander and Mac?edo(2016). We establish some theoretical results on applying the gauge duality theory to robust principal component analysis(PCA) and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Mac?edo(2016) from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.

基于RPCA的轴承表面缺陷视觉显著性检测

针对轴承缺陷图像存在的光照不均匀、整体对比度低、缺陷细节模糊等问题,结合鲁棒主成分分析和视觉显著性,提出一种新的轴承表面缺陷检测算法。首先,在鲁棒主成分的基础上,采用广朗日乘子算法计算稀疏矩阵,并根据稀疏矩阵计算缺陷区域的视觉显著值,生成凸显缺陷区域的显著图,然后,利用Otsu法对显著图进行缺陷分割,得到缺陷检测结果。并进行对比实验研究,结果表明,该检测方法能够显著突出轴承表面缺陷区域,实现对轴承表面各类缺陷的有效检测,与其他几种显著性检测方法相比,具有较好的查准率和召回率。

基于RPCA及低秩表示的气液两相流动图像中气泡图像分离研究

气液两相流中对气泡的测量研究是非常重要的,气泡测量技术中,如何实现气泡与背景分离是研究的重点问题。现有的测量技术大多采用图像二值化、边缘检测、图像滤波等方法来实现气泡信息的提取,而这些测量方法往往是存在不足的,仅仅针对单一图片或者需要人为手动选取。本文通过SVD(单值分解)和RPCA(鲁棒主成分分析法)对气液两相流中的气泡图像进行背景分离,其方法主要有两个特点:连续相关性和自动获取性。并提出逐行累加和逐列累加的方法,测量气泡的运动过程形态。研究表明,相比于原始的图像分离技术,利用RPCA运算,对气泡的定位、大小和速度表示都更准确。

基于RPCA的地基SAR近距强耦合信号抑制算法研究

地基合成孔径雷达(GBSAR)是一种全天时全天候非接触式大面积区域高精度形变监测手段,在矿区、边坡、大坝等区域的监测具有广泛应用。在封闭空间监测站中对外场进行连续监测时,雷达接收的回波信号会受到封闭空间的强散射信号干扰。近距离强散射信号耦合到雷达接收端形成虚假目标,严重影响成像质量。该文提出使用RPCA算法,在距离多普勒域将回波信号分解为低秩和稀疏两部分,利用距离多普勒域耦合信号的低秩特性,以及场景信号的稀疏特性,将耦合信号与场景信号有效分离。不同于基于PCA的已有耦合信号抑制方法,RPCA对场景回波信号本身没有高斯分布假设要求,这一假设要求在实际中通常是不满足的。此外,该文提出基于相关性分析的RPCA正则化系数优化选择方法,以实现低秩与稀疏的较优分离。该文通过实际GBSAR数据处理验证了方法的有效性,相比于已有的基于PCA的算法,基于RPCA的耦合信号抑制方法能够在保留场景回波信号的同时更好地抑制耦合信号。

基于RPCA低秩稀疏分解的循环频率检测方法

在强噪声干扰时循环频率的准确检测对于循环平稳信号处理有重要意义。该研究提出了一种低信噪比(signal-to-noise ratio, SNR)下将基于鲁棒主成分分析(robust principal component analysis, RPCA)的低秩稀疏分解技术应用于循环谱密度(cyclic spectral density, CSD)矩阵,从而进行循环频率检测的新方法。首先,采用RPCA将循环谱密度矩阵分解为表示噪声干扰的低秩矩阵和表示循环平稳特征的稀疏矩阵。随后,利用稀疏矩阵构造检测函数实现循环频率的自动检测。仿真结果证明了该方法在强噪声干扰下检测概率方面的优越性,并可根据检测各阶循环频率谐波的受试者工作特征(receiver operating characteristic, ROC)曲线为不同信噪比条件下选择检测阶数提供参考。为了进一步验证该方法在应用中的有效性,将该方法应用于滚动轴承的早期故障诊断中。滚动轴承加速疲劳寿命试验数据上的分析结果证明该方法能够在轴承早期故障阶段从低SNR的振动信号中准确检测出轴承的故障特征频率,实现轴承的早期故障诊断。

基于RPCA低秩模型的车辆外形识别研究

车辆外形识别作为车辆分类的依据具有重要现实应用价值。目前基于神经网络的车辆识别方法严重依赖于训练样本数量与质量,同时受限于训练时间长、泛化能力弱和可解释性差等不足。针对车辆外形识别问题,基于RPCA低秩模型,提出了利用低秩模型的车辆外形识别算法。首先,上述算法利用RPCA低秩模型提取出视频中目标物体的稀疏特征信息;然后,运用方向梯度直方图提取车辆的特征矩阵;最后,采用SVM分类器实现车辆外形的分类。实验结果表明,在较少的训练样本下,所提算法识别率或者准确率优于经典的PCA+SVM和Harr+AdaBoost算法,是一种可行的车辆外形识别算法。

基于结构相似度和鲁棒主成分分析的运动目标检测

运动目标传统检测方法只考虑图像的亮度或纹理等某一种特性,受特异值影响较大,对噪声比较敏感,鲁棒性也不够好,而且背景恢复精度不高。针对以上局限性,提出一种融合结构相似度(structural similarity,SSIM)全参考模型和鲁棒主成分分析(robust principal component analysis,RPCA)的运动目标检测方法。此方法综合考虑图像的亮度、对比度和结构三种特性,不采用传统的背景减除法,而是把图像像素点的结构相似度作为度量来实现运动对象与背景的分离。实验结果表明,此方法准确率可达0.95,且F度量较传统运动目标检测算法平均提升0.15,总体上比传统方法更具优势。

面向复杂场景的多通道慢速动目标稳健检测算法

针对鲁棒主成分分析(RPCA)算法在多通道慢速地面动目标指示(GMTI)中存在的高虚警以及对通道误差敏感问题,该文提出一种数据重构与速度合成孔径雷达(VSAR)-RPCA联合处理的方法。首先,通过样本挑选与联合像素法完成通道间数据精确重构;然后结合VSAR检测模式提出一种新的RPCA优化模型,通过采用交替投影乘子法对其进行求解得到空间频域的稀疏矩阵,进一步利用动目标与强杂波残余在空间频域通道的分布特性差异实现强杂波残余剔除与动目标检测;最后采用沿航迹干涉算法估计目标径向速度完成动目标重定位。相较于传统RPCA算法,所提算法在非理想强杂波背景下的虚警率显著降低。理论分析与实测实验验证了所提算法的有效性。

基于深度子空间学习的焊缝缺陷检测方法

主成分分析网络(PCANet)是一个基于简化的卷积神经网络的深度子空间学习模型。针对PCANet算法应用于焊缝缺陷检测时无法体现数据完整结构信息、对噪声较敏感等问题,在PCANet的基础上提出一种鲁棒非贪婪双向二维PCANet(RNG-BDPCANet)焊缝缺陷在线检测方法。RNG-BDPCANet在范数距离度量标准下,利用双向二维主成分分析作卷积核,并采用非贪婪策略得到目标函数最优的整体投影矩阵,对离群值具有较强的鲁棒性。最后,在自建的焊缝人工数据集、ORL和Yale B人脸数据集上分别进行实验。结果表明,所提出的算法在分类性能方面得到显著提高,具有较强的鲁棒性能。

基于RPCA的太阳能电池片表面缺陷检测

目前太阳能电池片生产过程中的缺陷检测主要由人工完成,费时费力,容易受主观因素的影响.文中提出了一种基于RPCA(Robust Principal Component Analysis,RPCA)的太阳能电池片表面缺陷检测方法.该方法对图像矩阵进行变换,使之分解成无缺陷的低秩矩阵图像和有缺陷的稀疏矩阵图像.通过凸优化的方法,分别最小化上述两个矩阵的核范数和1范数,从而使矩阵得以有效快速地分解.同时,文中分别对优化的两种算法:加速逼近梯度(Accelerated Proximal Gradient,APG)法和非精确增广拉格朗日乘子(Inexact Augmented Lagrange Multiplier,IALM)法,在太阳能电池片缺陷检测的计算时间和迭代次数方面进行了比较.最后通过大量实验,证明了上述方法在检测太阳能电池片表面缺陷的可行性和有效性.

基于RPCA的图像模糊边缘检测算法

针对传统边缘检测方法未能在抗噪性能与边缘检测精度之间取得较好的权衡的问题,利用鲁棒主成分分析模型良好的矩阵恢复能力与图像模糊边缘检测算法较佳的边缘检测性能,提出一种基于RPCA的图像模糊边缘检测算法,将图像的边缘检测问题转化为图像主成分的边缘检测问题。该算法对含噪图像进行RPCA分解,得到对应的稀疏图像和低秩图像,再用一种基于阈值的隶属函数将低秩图像转化至等效的模糊特征平面,并在该特征平面上进行模糊增强运算,最后进行空域转化及边缘提取等操作得到最终的边缘图像。实验结果表明,该算法提高了边缘定位的精度,对不同类型、不同强度的噪声均具有较好的抑制能力,适用于对实时性要求不高的图像处理。

基于全变分-核回归的RPCA运动目标检测方法

近年来,鲁棒主成分分析法(Robust Principal Component Analysis,RPCA)被广泛应用到运动目标检测中,但该类方法未能有效利用运动目标的时空连续性先验,容易将动态背景误判为运动目标,且背景恢复精度不高.为此提出一种基于全变分-核回归的RPCA运动目标检测方法.该方法以RPCA为基础,利用3维全变分模型增强前景的时空连续性,去除动态背景干扰,得到清晰完整的前景.同时,利用基于扩散张量的核回归对背景的时空相关性建模,去除噪声干扰,从而精确恢复背景.在多组公开数据集上的实验结果表明,该方法在动态背景、光照变化等复杂场景中能够较为精确地检测出运动目标和恢复背景.