相对主元分析及其在数据压缩和故障诊断中的应用研究

传统主元分析(Principal component analysis, PCA)方法因忽视量纲对系统的影响, 从而使选取的主元难以具有代表性; 而在进行量纲标准化后, 又因得到的特征值常常是近似相等的而无法进行有效的主元提取. 针对这一主要问题, 本文通过引入相对化变换(Relative transform, RT)、相对主元(Relative principal components, RPCs) 和分布"均匀"等概念, 建立起一种相对主元分析(Relative principal component analysis, RPCA)的新方法. 该方法首先对系统各分量进行量纲标准化; 其次再根据系统的先验信息分析和确定各分量的重要程度; 然后在系统能量守恒的准则下, 赋以系统各分量相应的权值; 最后利用已建立起的相对主元模型, 对系统实施RPCA. 同时运用数值例子, 开展了RPCA在数据压缩和系统故障诊断中的应用研究. 理论分析和仿真实验均表明, 采用RPCA方法选取出的主元更具代表性和显著几何意义, 加之选取主元的灵活性, 将使新方法具有更广泛的应用前景.     

基于SML特征检测的RPCA域多聚焦图像融合

针对多聚焦图像融合中难以有效检测聚焦点的问题,提出了一种基于鲁棒主成分分析（RPCA）和区域检测的多聚焦图像融合方法。将RPCA理论运用到多聚焦图像融合中,把源图像分解为稀疏图像和低秩图像;对稀疏矩阵采用区域检测的方法得到源图像的聚焦判决图;对聚焦判决图进行三方向一致性和区域生长法处理得到最终决策图;根据最终决策图对源图像进行融合。实验结果表明,在主观评价方面,所提出的方法在对比度、纹理清晰度、亮度等几方面都有显著的提高;在客观评价方面,用标准差、平均梯度、空间频率和互信息四项评价指标说明了该方法的有效性。     

利用数据低秩性和稀疏性的位场分离

鲁棒主成分分析将低维信号秩最小的单目标函数优化问题扩展成低维信号秩最小且高维信号稀疏的双目标函数优化问题。针对传统位场分离方法（如匹配滤波等）易出现欠拟合或过拟合现象，本文分析了区域场的低秩特征和局部场的稀疏特征，采用鲁棒主成分分析对位场进行分离，使得位场分离更加稳健。理论模型计算结果表明，该方法是一种有效、易于实现、权系数λ取值宽松的空间域方法，能够避免傅里叶变换带来的误差。最后将该方法用于宁夏卫宁北山地区重磁异常的处理解释，分离的局部低重、高磁异常与已知隐伏岩体对应关系好，并圈定了6个可能赋存隐伏岩体的异常区。     

Multi-focus image fusion based on sparse decomposition and background detection

The goal of image fusion is to accurately and comprehensively describe complementary information of multiple source images in a new scene. Traditional fusion methods are easy to produce side-effects which cause artifacts and blurred edges. To solve these problems, a novel fusion algorithm based on robust principal component analysis (RPCA) and guided filter is proposed. The guided filter can preserve the edges effectively, which is often used to enhance the images without distort the details. Considering edges and flat area are treated differently by the guided filter, in this paper, sparse component of the source image is filtered by the guided filter to generate the enhanced image which contains the preserved edges and the enhanced background. And then the focused regions of the source images are detected by spatial frequency map of the difference images between the enhanced image and the corresponding source image. Finally, morphological algorithm is used to obtain precise fusion decision map. Experimental results show that the proposed method improves the fusion performance obviously which outperforms the current fusion methods.     

基于多尺度训练库与多特征融合的人脸识别

针对光照差异、表情变化、遮挡等因素造成人脸识别率低的问题,提出一种基于多尺度训练库和加权特征的鲁棒性人脸识别算法。首先根据不同大小的图片具有不同信息量的特点定义并建立多尺度训练库,然后采用RPCA方法对人脸图像进行分解,之后进行HMLBP特征和Eigenface特征提取,最后引入一个权重因子将两种特征进行加权融合,并采用基于稀疏表达的方法对人脸图像进行识别。实验结果表明,相比其他人脸识别算法,本文提出的算法对标准人脸库保持较高识别率,最高可达99%,同时对遮挡人脸库也具有较好的识别效果,鲁棒性较高。     

时空RPCA在复杂场景下的运动目标检测

在复杂动态背景下,鲁棒主成分分析模型(RPCA)容易将背景中动态背景误判为前景运动目标,导致运动目标检测精度不高。为解决该问题,提出一种基于非凸加权核范数的时空低秩RPCA算法。使用非凸加权核范数替代传统的核范数进行低秩约束,在观测矩阵上通过拉普拉斯特征映射得到时空图拉普拉斯矩阵,将得到的时空图拉普拉斯矩阵嵌入低秩背景矩阵以保持背景对噪声和离群值的鲁棒性。实验结果表明,所提模型在复杂场景中能较准确检测出运动目标。     

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.     

基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

针对传统低秩表示聚类方法存在的稀疏性不足及噪声敏感等问题,提出了一种基于局部图拉普拉斯约束的鲁棒低秩表示聚类模型. 一方面,通过加入图像数据局部相似性的约束,在保持表示矩阵分块对角的特性下,增强了其稀疏性;另一方面,从数据相关性的角度分析了低秩表示模型的聚类性质, 通过采用鲁棒低秩表示模型,不仅降低了噪声的干扰,而且减弱了表示字典数据之间的线性相关性,从理论上保证了最终的邻接矩阵具有分块对角的良好聚类性质. 与传统低秩表示方法相比,本文得到的表示矩阵既保证了分块性质,又更加稀疏,仿真实验结果表明聚类效果有明显提升.     

牛顿-软阈值迭代鲁棒主成分分析算法

针对鲁棒主成分分析（RPCA）问题，为了降低RPCA算法的时间复杂度，提出了牛顿-软阈值迭代（NSTI）算法。首先，使用低秩矩阵的Frobenius范数与稀疏矩阵的l₁-范数的和来构造NSTI算法的模型；其次，同时使用两种不同的优化方式求解模型的不同部分，即用牛顿法快速计算出低秩矩阵，用软阈值迭代算法快速计算出稀疏矩阵，交替使用这两种方法计算出原数据的低秩矩阵和稀疏矩阵的分解；最后，得到原始数据的低秩特征。在数据规模为5 000×5 000，低秩矩阵的秩为20的情况下，NSTI算法和梯度下降（GD）算法、低秩矩阵拟合（LMaFit）算法相比，时间效率分别提高了24.6%、45.5%。对180帧的视频前景背景进行分离，NSTI耗时3.63 s，时间效率比GD算法、LMaFit算法分别高78.7%、82.1%。图像降噪实验中，NSTI算法耗时0.244 s，所得到的降噪后的图像与原始图像的残差为0.381 3，与GD算法、LMaFit算法相比，时间效率和精确度分别提高了64.3%和45.3%。实验结果证明，NSTI算法能够有效解决RPCA问题并提升RPCA算法的时间效率。     

Object tracking via online low rank representation

Object tracking is an active research topic in computer vision. The traditional tracking methods based on the generative model are sensitive to noise and occlusion, which leads to the failure of tracking results. In order to solve this problem, the tracking results of the first few frames are used as the observation matrix, and the low rank features of the observation model are solved by the the RPCA model. When the new video streams come, a new incremental RPCA is proposed to compute the new observation matrix by the augmented Lagrangian algorithm. The tracking model is established in the Bayesian framework, and the dictionary matrix is updated with the low rank feature. We have tested the proposed algorithm and six state-of-the-art approaches on eight publicly available sequences. Experimental results show that the proposed method has a lower pixel center position error and a higher overlap ratio.