基于新概率密度函数的ICA盲源分离

基于独立分量分析(Independent Component Analysis,ICA),利用极大似然估计法,研究了超高斯和亚高斯的混合信号的盲源分离(Blind Sources Separation,BSS)问题.文中构造了一种新的、不同于以往文章中用来分离混合信号的概率密度函数(Probability Density Function,PDF).新构造的PDF无需改变函数中的参数值,可用来对于超高斯和亚高斯信号的概率密度进行估计(假设未知源信号是相互独立的).数值实验验证了新构造的PDF的可行性,与原算法相比,收敛时间和分离效果都得到了较大的改善.     

基于粒子群算法优化的独立分量分析算法

通过两组模拟信号对三种主流独立分量分析算法-JADE、FastICA、扩展Infomax算法的性能进行了对比分析,结果表明三种算法均无法完全分离超高斯源与亚高斯源形成的混合信号,FastICA算法对能量强弱差别大的混合信号失效。基于这一现象,提出了一种新的独立分量分析算法,以粒子群算法为优化工具,以分离矩阵为优化变量,最小化分离信号联合概率与边缘概率乘积的差值,并给出了具体的计算流程。仿真实验结果表明,该算法的性能显著优于上述三种独立分量分析算法。同时,新提出算法实施过程中不需要任何先验知识,相比其他三种ICA算法,更适合解决工程实际问题。最后,将该算法应用于对滚动轴承实验台实测信号的处理,通过对分离信号的分析实现了对滚动轴承故障类型的准确识别,进一步证明了算法的有效性。     

基于独立分量分析的欠定盲源分离方法

目前的欠定盲分离算法只能分离稀疏信号,对于不稀疏的信号分离效果不理想。经典独立分量分析算法中的扩展Infomax算法既能分离超高斯信号,也能分离亚高斯信号,但却只能应用于观测数不少于源数的超定盲源分离,结合扩展Infomax算法,本文提出了一种欠定ICA算法,通过生成隐藏数据将欠定盲分离问题转化为超定盲分离问题,然后再应用经典的扩展Infomax算法进行分析,该方法可以分离欠定情形下超高斯和亚高斯混合信号。并用该算法对实测的齿轮箱混合故障信号进行分离,再用包络阶次方法对分离出的信号进行分析,成功识别出了齿轮箱的不同故障特征,验证了该算法在齿轮箱故障诊断中的有效性。     

粒子滤波和独立分量分析的含噪信号盲分离算法研究

研究了两阶段含噪独立分量分析算法来解决含噪信号盲分离问题。第一阶段,通过粒子滤波实现对不含噪混合信号的估计,将含噪独立分量分析转化为不含噪的独立分量分析;第二阶段用现有的FastICA算法从估计的不含噪混合信号中提取出源信号。不含噪混合信号的时变自回归模型和含噪与不含噪混合信号之间的关系构造了动态的状态．空间方程。该方程的特点是多变量、过程和观测噪声不限于高斯分布,粒子滤波是解决该问题的有效方法。提出了解决含噪独立分量分析的PF＋FastICA算法,仿真试验表明所提出的算法性能优于相关文献的结果。     

基于平面聚类势函数法的欠定混合信号盲分离

针对不充分稀疏欠定混合信号盲分离,提出了一种基于超平面聚类的势函数法来估计源信号个数和混合矩阵。该方法在源信号个数未知的情况下,利用聚类平面法线向量构成势函数,通过估计势函数的局部最大值来估计聚类平面的法线向量,然后再通过估计聚类平面的交线来实现混合矩阵的估计。为了提高算法对异常值的鲁棒性,不直接估计势函数的局部最大值,而是采用聚类算法来估计势函数的局部最大值。计算机仿真试验证实了该算法的有效性及其较好的性能。     

基于核竞争学习算法的图像特征提取

利用核函数学习可有效解决图像特征线性不可分的特性,结合稀疏表示算法的优势,提出了一种新的图像特征提取方法。采用基于竞争学习规则的独立分量分析法对图像进行稀疏表示,该算法可提取数据的高维特征,且不需要优化高阶的非线性函数和进行稀疏密度估计,因而有较快的收敛速度。与仅使用基于竞争学习的独立分量分析法相比,在PolyU数据库上的实验结果表明,采用基于核函数学习和稀疏表示相结合的方法所提取的数据特征有利于提高特征分类精度。     

一种新的相关机械振源盲分离方法

针对传统盲源分离算法在机械振源不满足统计独立特性时,无法有效分离出振源信号的问题,提出了基于信号稀疏特性的相关机械源盲分离方法。盲源分离算法的关键在于准确地估计出混合矩阵。因此,首先提出了不相关源混合矩阵的估计方法;然后针对相关源,提出了有效剔除相关成分的方法,使得剩余信号可以按照不相关源进行处理。通过理论分析、仿真验证以及实测数据分析,验证了该方法的有效性。     

基于相似性函数的稀疏成分分析混合矩阵估计方法

稀疏成分分析是信号处理中解决欠定盲源分离问题的新方法,本文研究了稀疏成分分析中的混合矩阵估计问题,提出了无需预知源个数利用一种相似性函数估计混合矩阵的方法。首先,估计相似性函数中的核参数,使得算法适应不同的稀疏信号。然后,给出了估计混合矩阵的不动点算法。最后,实验结果表明提出的算法通过适当地选取参数,能够准确有效地估计出具有不同源个数的混合矩阵,对不太稀疏的源也有令人满意的结果。     

基于稀疏分解的多分量线性调频信号参数估计∗

本文提出了一种多分量线性调频信号的参数估计方法。基于过完备Gabor字典的Matching Pursuit算法,可以将信号表示为Gabor原子的线性组合。这些原子有效的揭示了信号的内在时频结构特征,是信号的一种稀疏表示。本文直接利用分解得到的稀疏信息对信号中调频分量的调频率、初始频率和结束频率进行估计。仿真结果显示,该方法适用于存在强有意干扰或者有色噪声的环境。     

基于时域随机化的超高斯真随机驱动信号生成技术研究

提高振动模拟试验的真实性和增强振动激发试验的效力都需要产生超高斯分布的真随机驱动信号。研究了基于时域随机化的超高斯真随机驱动信号生成技术,针对常用半正弦窗函数和不同重叠因子值进行了理论分析和数值仿真,结果表明:时域随机化前后的伪随机和真随机信号峭度值是线性关系,但输出的超高斯真随机信号峭度值比输入的超高斯伪随机信号峭度值要小,并且重叠因子取值越大峭度值减小的程度越大。     

基于模型稀疏表示的单快拍波达方向鲁棒估计

基于传感器阵列输出模型的稀疏重构,研究了利用单快拍数据进行波达方向（Direction of Arrival,DOA）估计的问题。考虑到在实际应用中,目标信号个数远小于传感器阵元数,目标信号DOA相对于空间来说也是稀疏的,将传统的传感器阵列输出模型进行稀疏化表示,得到阵列输出数据的稀疏表示模型,研究了一种基于l₁-范数最小化的单快拍DOA估计算法（L1-Min）。该算法将稀疏参数求解问题转化为二阶锥规划（Second-Order Cone Programming,SOCP）问题的一般形式,并在二阶锥规划的框架下求解,同时分析了算法中正则化参数的选取依据。L1-Min算法对小样本、相干多径信号、目标信号角度间隔小等非理想条件都具有较好的鲁棒性。仿真实验验证了算法的有效性。     

独立分量分析的图像融合算法

独立分量分析可实现图像的稀疏编码并具有能很好地捕捉图像重要边缘信息的特性.本文提出一种基于独立分量分析的图像融合算法,结合支持向量机对多聚焦图像的清晰域、模糊域进行判断以及在ICA域中进行图像分割以提取图像的主要边缘特征信息来实现特征级的多聚焦图像的融合.实验结果表明,本文提出的融合算法是有效的.     

基于压缩感知的多中继协作通信系统稀疏信道估计算法研究

提出了一种基于压缩感知理论的多中继协作通信系统稀疏信道估计方法.采用正交匹配追踪（Orthogonal Matching Pursuit,OMP）压缩感知算法,对时域信道脉冲响应进行估计.对多中继协作通信系统进行稀疏建模;结合压缩感知理论构建观测矩阵,并给出卷积信道的稀疏表示;利用压缩信道感知算法重建了系统的卷积复合信道.仿真结果表明,与传统的最小二乘法（Least Square,LS）相比,采用压缩感知理论的信道估计算法,能利用较少的导频信号获得很好的信道估计性能,提高了频谱利用率.     

Multiscale ICA for fundus image analysis

Independent component analysis is a technique used for separation of statistically independent sources. It can estimate unknown sources from a mixture of sources without any prior knowledge about them. The sources should be non‐Gaussian and independent with each other. In this work, multiscale ICA is proposed for medical images (fundus images, MRI Images). The data matrix is formed by considering the higher sub‐bands of multiscale decompositions. Performance of multiscale ICA is evaluated and compared with the ICA algorithms using simulated signals and different medical images using Amari performance index and Comon test values. Results show that API and Comon test values are less for multiscale ICA for simulated signals. In case of pathological images, the features are separated correctly by multiscale ICA. Multiscale ICA performs better than simple ICA for separation and detection of independent components from medical images (fundus images), such as blood vessels and artifacts. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 327–337, 2013     

Chromatic structure of natural scenes

We applied independent component analysis (ICA) to hyperspectral images in order to learn an efficient representation of color in natural scenes. In the spectra of single pixels, the algorithm found basis functions that had broadband spectra and basis functions that were similar to natural reflectance spectra. When applied to small image patches, the algorithm found some basis functions that were achromatic and others with overall chromatic variation along lines in color space, indicating color opponency. The directions of opponency were not strictly orthogonal. Comparison with principal-component analysis on the basis of statistical measures such as average mutual information, kurtosis, and entropy, shows that the ICA transformation results in much sparser coefficients and gives higher coding efficiency. Our findings suggest that nonorthogonal opponent encoding of photoreceptor signals leads to higher coding efficiency and that ICA may be used to reveal the underlying statistical properties of color information in natural scenes.     

Sparse electrocardiogram signals recovery based on solving a row echelon‐like form of system

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two‐stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon‐like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.Inspec keywords: electrocardiography, matrix algebra, medical signal processingOther keywords: sparse electrocardiogram signal recovery, row echelon‐like form of system, noise environment, biological data analysis, personalised medicine, dictionary learning algorithm, transformation matrices, sparse biomedical signal recovery     

Application of independent component analysis with mixture density model to localize brain alpha activity in fMRI and EEG

Independent component analysis (ICA) is an approach to solve the blind source separation problem. In the original and extended versions of ICA, nonlinearity functions are fixed to have specific density forms such as super‐Gaussian or sub‐Gaussian, thereby limiting their performance when sources with different classes of densities are mixed in multichannel data. In this article, we have incorporated a mixture density model such that no assumption about source density would be required. We show that this leads to better source separation due to increased flexibility in handling source‐ densities with flexible parametric nonlinearity. The algorithm was validated through simulation studies and its performance was compared to other versions of ICA. The modified mixture density ICA was then applied to functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) data to localize independent sources of alpha activity in the human brain. A good spatial correlation was found in the spatial distribution of alpha sources derived independently from fMRI and EEG, suggesting that spontaneous alpha rhythm can be imaged by fMRI using ICA without concurrent acquisition of EEG. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol 14, 170–180, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20021     

Reconstructing gas distribution maps via an adaptive sparse regularization algorithm

In this paper, we present an algorithm to be used by an inspection robot to produce a gas distribution map and localize gas sources in a large complex environment. The robot, equipped with a remote gas sensor, measures the total absorption of a tuned laser beam and returns integral gas concentrations. A mathematical formulation of such measurement facility is a sequence of Radon transforms, which is a typical ill-posed problem. To tackle the ill-posedness, we develop a new regularization method based on the sparse representation property of gas sources and the adaptive finite-element method. In practice, only a discrete model can be applied, and the quality of the gas distribution map depends on a detailed 3-D world model that allows us to accurately localize the robot and estimate the paths of the laser beam. In this work, using the positivity of measurements and the process of concentration, we estimate the lower and upper bounds of measurements and the exact continuous model (mapping from gas distribution to measurements), and then create a more accurate discrete model of the continuous tomography problem. Based on adaptive sparse regularization, we introduce a new algorithm that gives us not only a solution map but also a mesh map. The solution map more accurately locates gas sources, and the mesh map provides the real gas distribution map. Moreover, the error estimation of the proposed model is discussed. Numerical tests for both the synthetic problem and practical problem are given to show the efficiency and feasibility of the proposed algorithm.     

OFDM水声通信系统的LS-OMP信道估计

对于正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)水声通信系统,最小二乘(Least Squares,LS)信道估计方法受噪声影响较大,并且使用的导频数量较多,影响通信效率。而基于压缩感知理论的正交匹配追踪(Orthogonal Matching Pursuit,OMP)信道估计方法可以充分利用水声信道的稀疏特性,同时能够有效地抑制系统噪声,但控制迭代运算次数的相关参数(稀疏度或误差容忍值)是OMP算法的关键条件。针对上述问题,提出了利用少量导频随机分布的LS和OMP联合的信道估计方法,该方法首先利用少量导频采用LS方法估计出OMP算法的误差容忍值,再利用OMP算法恢复数据子载波的信道信息。理论分析和仿真结果同时表明,与传统的LS算法或OMP算法相比,新算法能够在数据恢复的同时有效抑制系统噪声,应用稀疏特性及较少量的导频,进一步提高了系统的频谱效率,对时变稀疏水声信道具有更好的适应性。     

State-space independent component analysis for nonlinear dynamic process monitoring

The cost effective benefits of process monitoring will never be over emphasised. Amongst monitoring techniques, the Independent Component Analysis (ICA) is an efficient tool to reveal hidden factors from process measurements, which follow non-Gaussian distributions. Conventionally, most ICA algorithms adopt the Principal Component Analysis (PCA) as a pre-processing tool for dimension reduction and de-correlation before extracting the independent components (ICs). However, due to the static nature of the PCA, such algorithms are not suitable for dynamic process monitoring. The dynamic extension of the ICA (DICA), similar to the dynamic PCA, is able to deal with dynamic processes, however unsatisfactorily. On the other hand, the Canonical Variate Analysis(CVA) is an ideal tool for dynamic process monitoring, however is not sufficient for nonlinear systems where most measurements follow non-Gaussian distributions. To improve the performance of nonlinear dynamic process monitoring, a state space based ICA (SSICA) approach is proposed in this work. Unlike the conventional ICA, the proposed algorithm employs the CVA as a dimension reduction tool to construct a state space, from where statistically independent components are extracted for process monitoring. The proposed SSICA is applied to the Tennessee Eastman Process Plant as a case study. It shows that the new SSICA provides better monitoring performance and detect some faults earlier than other approaches, such as the DICA and the CVA.