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.

Sparse flight spotlight mode 3-D imaging of spaceborne SAR based on sparse spectrum and principal component analysis

The spaceborne synthetic aperture radar(SAR)sparse flight 3-D imaging technology through multiple observations of the cross-track direction is designed to form the cross-track equivalent aperture,and achieve the third dimensionality recognition.In this paper,combined with the actual triple star orbits,a sparse flight spaceborne SAR 3-D imaging method based on the sparse spectrum of interferometry and the principal component analysis(PCA)is presented.Firstly,interferometric processing is utilized to reach an effective sparse representation of radar images in the frequency domain.Secondly,as a method with simple principle and fast calculation,the PCA is introduced to extract the main features of the image spectrum according to its principal characteristics.Finally,the 3-D image can be obtained by inverse transformation of the reconstructed spectrum by the PCA.The simulation results of 4.84 km equivalent cross-track aperture and corresponding 1.78 m cross-track resolution verify the effective suppression of this method on high-frequency sidelobe noise introduced by sparse flight with a sparsity of 49%and random noise introduced by the receiver.Meanwhile,due to the influence of orbit distribution of the actual triple star orbits,the simulation results of the sparse flight with the 7-bit Barker code orbits are given as a comparison and reference to illuminate the significance of orbit distribution for this reconstruction results.This method has prospects for sparse flight 3-D imaging in high latitude areas for its short revisit period.

Compressive Sensing Sparse Sampling Method for Composite Material Based on Principal Component Analysis

Signals can be sampled by compressive sensing theory with a much less rate than those by traditional Nyquist sampling theorem,and reconstructed with high probability,only when signals are sparse in the time domain or a transform domain.Most signals are not sparse in real world,but can be expressed in sparse form by some kind of sparse transformation.Commonly used sparse transformations will lose some information,because their transform bases are generally fixed.In this paper,we use principal component analysis for data reduction,and select new variable with low dimension and linearly correlated to the original variable,instead of the original variable with high dimension,thus the useful data of the original signals can be included in the sparse signals after dimensionality reduction with maximize portability.Therefore,the loss of data can be reduced as much as possible,and the efficiency of signal reconstruction can be improved.Finally,the composite material plate is used for the experimental verification.The experimental result shows that the sparse representation of signals based on principal component analysis can reduce signal distortion and improve signal reconstruction efficiency.

Ground-roll separation of seismic data based on morphological component analysis in twodimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation.In this study,according to differences in morphological characteristics between ground roll and reflected waves,we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves.Because ground roll is characterized by lowfrequency,low-velocity,and dispersion,we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll.Because of a strong local correlation of the reflected wave,we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves.A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model,strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.

Text Detection in Natural Scene Images Using Morphological Component Analysis and Laplacian Dictionary

Text in natural scene images usually carries abundant semantic information. However, due to variations of text and complexity of background, detecting text in scene images becomes a critical and challenging task. In this paper, we present a novel method to detect text from scene images. Firstly, we decompose scene images into background and text components using morphological component analysis(MCA), which will reduce the adverse effects of complex backgrounds on the detection results.In order to improve the performance of image decomposition,two discriminative dictionaries of background and text are learned from the training samples. Moreover, Laplacian sparse regularization is introduced into our proposed dictionary learning method which improves discrimination of dictionary. Based on the text dictionary and the sparse-representation coefficients of text, we can construct the text component. After that, the text in the query image can be detected by applying certain heuristic rules. The results of experiments show the effectiveness of the proposed method.

Application of Decomposition and Denoising of Gearbox Signal Based on Morphological Component Analysis

Morphological component analysis( MCA) is a signal separation method based on signal morphological diversity and sparse representation. MCA can extract the signal components of different morphologies by different dictionary combinations. Firstly,the theory of MCA was analyzed with sparse representation principle and relaxation criterion. Then detailed steps of block coordinate relaxation( BCR) were given. Finally,algorithm performance was verified by simulation signals analysis, MCA was applied to decomposing and denoising gearbox signals, and the fault parameters were extracted by energy operator demodulation envelop of morphological component.

Seismic data denoising under the morphological component analysis framework combined with adaptive K-SVD and wave atoms dictionary

Many different effective reflection information are often contaminated by exterior and random noise which concealed in the seismic data.Traditional single or fixed transform is not suit for exploiting their complicated characteristics and attenuating the noise.Recent years,a novel method so-called morphological component analysis(MCA)is put forward to separate different geometrical components by amalgamating several irrelevance transforms.According to study the local singular and smooth linear components characteristics of seismic data,we propose a method of suppressing noise by integrating with the advantages of adaptive K-singular value decomposition(K-SVD)and wave atom dictionaries to depict the morphological features diversity of seismic signals.Numerical results indicate that our method can dramatically suppress the undesired noises,preserve the information of geologic body and geological structure and improve the signal-to-noise ratio of the data.We also demonstrate the superior performance of this approach by comparing with other novel dictionaries such as discrete cosine transform(DCT),undecimated discrete wavelet transform(UDWT),or curvelet transform,etc.This algorithm provides new ideas for data processing to advance quality and signal-to-noise ratio of seismic data.

Adaptive blind separation of underdetermined mixtures based on sparse component analysis

The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

Block principle and pattern classification component analysis （BPCA） is a recently developed technique in computer vision In this paper, we propose a robust and sparse BPCA with Lp-norm, referred to as BPCALp-S, which inherits the robustness of BPCA-L1 due to the employment of adjustable Lp-norm. In order to perform a sparse modelling, the elastic net is integrated into the objective function. An iterative algorithm which extracts feature vectors one by one greedily is elaborately designed. The monotonicity of the proposed iterative procedure is theoretically guaranteed. Experiments of image classification and reconstruction on several benchmark sets show the effectiveness of the proposed approach.

Inverse synthetic aperture radar imaging based on sparse signal processing

Based on the measurement model of inverse synthetic aperture radar (ISAR) within a small aspect sector,an imaging method was presented with the application of sparse signal processing.This method can form higher resolution inverse synthetic aperture radar images from compensating incomplete measured data,and improves the clarity of the images and makes the feature structure much more clear,which is helpful for target recognition.The simulation results indicate that this method can provide clear ISAR images with high contrast under complex motion case.

A contourlet-transform based sparse ICA algorithm for blind image separation

A contourlet-transform （CT） based sparse independent component analysis for blind image separation is proposed. The images are first decomposed into sets of local features with various degrees of sparsity, and then the intrinsic property is used to select the best （sparsest） subsets of features for further separation. Based on sparse description of the contourlet- transform, the proposed approach is able to yield better performance, including faster convergence and the certain order for the separated signals. Simulation results confirm the validity of the proposed method.

Color Estimation for Thermal Infrared Imagery Based on Kernel PCA and Sparse Representation

Adding colors to monochrome thermal infrared images can help observers understand the scenery better. A nonlinear color estimation method for single-band thermal infrared imagery based on kernel principal component analysis (KPCA) and sparse representation was proposed. Nonlinear features of infrared image were extracted using KPCA. The relationship between image features and chromatic values was learned using sparse representation and a color estimation model was obtained. The thermal infrared images can be rendered automatically using the color estimation model. The experimental results show that the proposed method can render infrared image with an accurate color appearance. The proposed idea can also be used in other color estimation problem.

基于多形态学成分分析的图像融合

将多尺度分解与稀疏表示相结合,提出了一种基于多形态学成分分析(MCA)的图像融合算法。采用基于联合稀疏表示(JSR)的方法融合卡通子图像中的冗余和互补信息,并利用基于方向特征的方法融合具有更多细节信息和噪声的纹理子图像。结果表明,提出的图像融合算法在主观视觉效果和客观评价指标上均优于先进的图像融合算法。

基于非凸正则化与稀疏成分分析的复合故障诊断方法

用于解决多故障问题的复合故障诊断技术是企业设备状态监测与故障诊断的关键环节之一。大型机械和设备群组在经过较长时间的服役期后,由于经常在高温、大载荷等工况条件比较复杂的环境下运行,核心部件难免发生由不同损伤组成的复合故障从而使得设备故障的诊断困难。为解决上述问题,提出一种新型的基于非凸正则化与稀疏成分分析的复合故障诊断方法,通过构造非凸惩罚函数以提高信号的稀疏性,并确保目标函数的全局凸性,从而尽可能地提高稀疏成分分析方法的准确度。该方法可以在预先不知道故障源数量的情况下,通过构建一个稀疏优化框架以确保诊断结果的准确性,从而解决滚动轴承的多故障诊断问题。通过仿真实验对所提方法进行验证,基于非凸正则化的均方根误差(RMSE)最优值小于0.5,故障特征更为明显,优于传统方法。以900 r/min和1 300 r/min的轴承故障实验为例,外圈、内圈、滚动体特征频率均可准确识别,表明所提方法可以有效进行复合故障的诊断。

结构运营模态参数识别的稀疏分量分析新方法

结合时频掩码技术和模糊C均值聚类,提出一种结构运营模态参数识别新方法。该方法根据结构振动响应的能量信息建立时频掩码,通过时频掩码求解结构模态响应,采用单自由度模态参数识别技术从模态响应中识别模态频率和阻尼比。结构振动响应能量峰值处的时频系数被依次提取,经单源点检测后采用模糊C均值聚类对其聚类,将第一个聚类中心作为模态振型。通过数值案例和框架结构试验验证所提方法的有效性。结果表明,所提方法具有良好的模态参数识别精度和噪声鲁棒性。

噪声干扰下基于PCA-SF的轴承故障诊断方法

机械故障诊断对降低维修成本和预防事故至关重要。振动信号监测是机械故障诊断中一种有效可行的方法。然而,所采集故障信号往往容易受到其他设备噪声的干扰。因此,从受噪声干扰的监测信号中提取与故障相关的周期脉冲是故障诊断的基础,也是难点。为解决此问题,提出一种基于主成分分析(Principal Component Analysis,PCA)和稀疏滤波(Sparse Filtering,SF)的机械故障特征提取方法。具体来说,首先利用PCA提取噪声干扰信号段的主成分,然后利用SF从主成分中提取有效特征。为减小SF模型的过拟合问题,采用L1/2范数对其目标函数进行正则化约束。最后,将提取的特征输入到Softmax分类器中进行故障识别。分别通过一组仿真和实验案例对所提PCA-SF方法的有效性进行验证。实验结果表明,该方法不仅能准确实现故障分类,而且优于其他传统方法。

基于稀疏学习的电力大数据压缩与高精度重建

电网的运行需要大量电力大数据的支持,为了降低传输工作量,设计基于稀疏学习的电力大数据压缩与高精度重建方法。采用最优复杂度模型处理电力大数据的缺失值,通过基于残差学习方法的DnCNN去噪模型,对大数据去噪。根据向量主成分分析方法,对电力大数据进行压缩处理。基于稀疏学习构建大数据重建网络模型,实现电力大数据的重建。实验测试结果表明,设计方法的数据压缩比最高达到0.986,综合矢量误差整体低于0.3%,归一化均方误差整体低于0.8%。

面向阶段任务的携行器材品种确定方法

维修器材是有效实施维修保障的物质基础,携行器材品种确定是开展维修器材携行决策的关键。针对执行阶段任务武器装备维修器材品种多、影响因素复杂且关联关系不明确造成的携行器材品种确定困难的现实问题,提出了一种将改进稀疏核主成分分析(sparse kernel principal component analysis,SKPCA)算法与长短时记忆(long short-term memory,LSTM)神经网络模型相结合的阶段任务携行器材品种确定方法。在分析与任务阶段时序相关的携行器材影响因素及特征指标的基础上,运用基于弹性惩罚的SKPCA降维算法,对器材特征进行降维分析并得到低维稀疏特征向量,通过缩减数据容量增强特征指标的可解释性;运用混沌序列改进花授粉算法(flower pollination algorithm,FPA)优化LSTM超参数,构建混沌FPA-LSTM预测模型,精准进行携行器材品种确定。通过对演习携行器材品种确定算例分析验证了所提方法的科学性和可行性。

基于改进K-means聚类的电网抢修资源优化技术

针对传统电网抢修资源配置中存在主观性强、处理突发状况能力较弱的问题,文中基于改进K-means聚类算法提出了一种电网抢修资源的分配策略。该策略采用改进算法分析平台的工单数据,以获得聚合数据包,并利用主成分分析法完成对数据的降维。降维后的数据经过深度稀疏自编码器的训练,得到的数据特征被K-means++算法聚类,进而输出工单任务的优先级。所提改进算法考虑了多种复杂因素的影响,相比传统算法其综合性能更为理想。多项实验结果表明,所提算法的聚类性能和数据训练性能在多个对比算法中均为最优,可以准确地识别出测试用例中的任务等级,为电网抢修资源的分配与决策提供技术支撑。