Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

In this paper, a new method to reduce noises within chaotic signals based on ICA(independent component analysis)and EMD(empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions(IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals.Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor.     

基于非线性时间序列分析经验模态分解和小波分解异同性的研究

基于经验模态分解(EMD）的希尔伯特变换（HT），是对非线性时间序列基于EMD进行分解， 然后通过HT获得频谱.利用理想时间序列和青藏高原古里雅冰芯¹⁸O时 间序列 ，系统地分析比较了EMD和小波分解(WD）以及HT和小波变换在非线性时间序列处理中的优劣 ，并针对它们各自的缺点提出了可能改进的设想.研究结果表明，将基于EMD的方法和基于WD 的方法有机结合起来应用，可以更有效地识别原时间序列的特征信息. 关键词： 经验模态分解 小波分解 理想时间序列 古里雅冰芯     

Comparison of simultaneous signals obtained from a dual-field-of-view lidar and its application to noise reduction based on empirical mode decomposition

Although the empirical mode decomposition (EMD) method is an effective tool for noise reduction in lidar signals, evaluating the effectiveness of the denoising method is difficult. A dual-field-of-view lidar for observing atmospheric aerosols is described. The backscattering signals obtained from two channels have different signal-to-noise ratios (SNRs). The performance of noise reduction can be investigated by comparing the high SNR signal and the denoised low SNR signal without a simulation experiment. With this approach, the signal and noise are extracted to one intrinsic mode function (IMF) by the EMD- based denoising; thus, the threshold method is applied to the IMFs. Experimental results show that the improved threshold method can effectively perform noise reduction while preserving useful sudden-change information.     

基于经验模态分解和小波阈值的冲击信号去噪

冲击信号是非线性的并且容易受到噪声污染。为研究冲击信号去噪的问题,本文针对经验模态分解(Empirical Mode Decomposition,EMD)去噪和小波阈值去噪方法存在的不足,提出了基于EMD的小波阈值去噪方法。单纯的EMD去噪方法会在去除高频噪声的同时压制高频的有效信息。本文将EMD与小波阈值去噪相结合,利用连续均方误差准则确定含噪较多的高频固有模态函数(Intrinsic Mode Function, IMF),对高频IMF分量进行小波阈值去噪,以分离并保留这些分量中的有效信息,同时保持低频IMF分量不变。对模拟数据和实际冲击信号进行去噪处理,结果表明,基于EMD的小波阈值去噪方法的去噪效果优于单纯的EMD去噪方法和小波阈值去噪方法。     

基于经验模态分解的高光谱遥感数据去噪方法

经验模态分解(EMD)是一种新的时频分析方法,经EMD分解后的各个固有模态函数(IMF)突出了原始信号的局部特征,从而可以区分噪声和有用信号。基于此,结合高光谱遥感数据的光谱变化特征,提出了一种基于经验模态分解的高光谱遥感数据去噪方法。通过对理论数据的实验表明,数据中的噪声无论是高斯分布还是均匀分布,数据经EMD分解后,噪声都主要集中在前几个特定的IMF,对相应的IMF进行滤波处理后并与其他IMF分量进行重构就可得到去噪信号,与小波去噪结果相比较,这种方法效果更好。最后把该去噪方法应用于野外实测的油膜高光谱数据去噪,实验结果表明,该方法能准确、有效地去除高光谱遥感数据的噪声。     

A Novel Noise Reduction Method of UAV Magnetic Survey Data Based on CEEMDAN,Permutation Entropy,Correlation Coefficient and Wavelet Threshold Denoising

Despite the increased attention that has been given to the unmanned aerial vehicle (UAV)-based magnetic survey systems in the past decade, the processing of UAV magnetic data is still a tough task. In this paper, we propose a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), permutation entropy (PE), correlation coefficient and wavelet threshold denoising. The original signal is first decomposed into several intrinsic mode functions (IMFs) by CEEMDAN, and the PE of each IMF is calculated. Second, IMFs are divided into four categories according to the quartiles of PE, namely, noise IMFs, noise-dominant IMFs, signal-dominant IMFs, and signal IMFs. Then the noise IMFs are removed, and correlation coefficients are used to identify the real signal-dominant IMFs. Finally, the wavelet threshold denoising is applied to the real signal-dominant IMFs, the denoised signal can be obtained by combining the signal IMFs and the denoised IMFs. Both synthetic and field experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can eliminate the interference to a great extent, which lays a foundation for the further interpretation of UAV magnetic data.     

脉冲星信号的经验模态分解模态单元比例萎缩消噪算法

针对脉冲星信号的消噪问题, 提出了一种基于模态单元比例萎缩的经验模态分解(EMD)消噪方法. 利用经验模态分解将含噪脉冲星信号分解为一组内蕴模态函数(IMF), 将IMF中两个过零点间的部分定义为模态单元, 以模态单元为基本单位构造最优比例萎缩因子, 对IMF中的每个模态单元进行比例萎缩去噪, 进而建立基于模态单元比例萎缩的脉冲星信号滤波模型.对含噪脉冲星信号进行了消噪实验分析, 实验结果表明, 与小波硬阈值消噪法、比例萎缩小波消噪法和基于模态单元阈值的EMD消噪法相比, 该方法可以更有效地去除脉冲星信号中的噪声, 同时更好地保留了原信号中的有用细节信息. 关键词： 经验模态分解 脉冲星信号 模态单元比例萎缩 消噪     

改进的经验模态分解法分离超声多普勒血流与管壁信号

超声多普勒血流信号常包含管壁信号的干扰,准确分离二者对提高血流检测的精度具有重要作用。本文提出两种改进的经验模态分解(EMD)方法,先将含管壁信号的超声多普勒信号分解成多层本征模态函数(IMF),然后根据血流信号与管壁信号的不同特性,对既含管壁信号又含血流信号的IMF分量进行分离处理,最后将各层IMF分量中的管壁成分叠加得到管壁信号的估计,而血流信号可通过原信号减去估计的管壁信号而得到。将本方法用于计算机仿真信号和人体实测的超声多普勒信号,并与高通滤波器法、空间选择性降噪法和原EMD法进行比较,结果表明:本文提出的两种方法能在较大的管壁搏动速度范围内准确地分离血流信号和管壁信号,其平均相对误差比高通滤波器的结果降低了约52%和57%。可见,本文提出的两种方法有望用于血流信号与管壁信号的准确分离。      

应用经验模态分解和独立成分分析解译岩矿光谱

岩矿光谱由多种矿物光谱混合而成,解译岩矿光谱能够得到岩矿的组分信息,且该方法具有快速、方便、不损坏样品的特点。经验模态分解(empirical mode decomposition, EMD)不能直接分离出混合信号中的源信号,独立成分分析(independent component analysis, ICA)要求混合信号数目不小于其所包括的源信号数目。将EMD和ICA两种方法相融合,首先用EMD分解混合信号得到本征模态函数(intrinsic mode function, IMF),再选择一定数目的IMF与混合信号一起组成ICA的输入数据矩阵,经过ICA运算可以获取单一混合信号中的源信号信息,克服了EMD和ICA两种方法各自的缺陷。研究表明,综合应用EMD和ICA方法可以获取单一混合信号中的源信号信息,混合信号中源信号含量越大,得到的源信号近似值越理想。参与ICA分离的IMF数目决定了分离得到的源信号近似值的数目,并且选择的IMF与混合信号相关系数越大,得到的源信号近似值越理想。运用该方法定量分析岩矿光谱,可以获取组成岩矿的矿物信息,比较适用于野外作业岩矿的快速分析鉴定及成分初步分析。     

基于改进经验模态分解域内心动物理特征识别模式分量的心电信号重建

心电图(electrocardiogram,ECG)诊断心脏疾病的严格标准,要求有效地消除噪声并准确地重建ECG信号.经验模式分解(empirical mode decomposition,EMD)方法重建ECG信号中,模式混叠及重建采用模式分量的识别以经验为基础,导致重建ECG信号准确度降低,且方法不具有自适应和通用性.本文首先基于积分均值定理提出一种改进的EMD方法——积分均值模式分解(integral mean mode decomposition,IMMD)方法,经5000个高斯白噪声样本的蒙特卡罗法验证,IMMD方法比EMD具有更优多分辨率分析能力,能够有效地缓解模式混叠.其次,基于ECG信号内固有心动物理特征量识别重建ECG信号所采用的模式分量,具有现实物理意义,因此,方法具有自适应和通用性.经验证,提出方法重建47例ECG信号与原ECG信号的相关系数中:31例优于变分模式分解方法;33例优于Haar小波软阈值法;42例优于集总经验模式分解方法;45例优于EMD方法.相关系数均值为0.8904,方差为0.0071,表现稳定且最优.     

噪声模态单元预判的经验模态分解脉冲星信号消噪

为了改善脉冲星辐射脉冲信号的消噪效果, 提出了一种基于噪声模态单元预判的经验模态分解(EMD) 消噪声方法. 该方法首先利用EMD将含噪辐射脉冲信号分解为一组内蕴模态函数(IMF), 根据IMF系数的统计特性采用局部均方误差准则进行噪声模态单元预判, 并将噪声模态单元置零; 然后对噪声模态单元预判处理后的IMF以模态单元为基本单位进行最优比例萎缩消噪, 从而达到抑制噪声、保留信号的目的. 实验结果表明: 与Sure Shrink小波阈值法、Bayes Shrink小波阈值法和EMD模态单元比例萎缩法相比, 基于噪声模态单元预判的EMD消噪方法可以更有效地去除脉冲辐射信号中的噪声, 同时更好地保留信号突变处的细节信息特征, 在信噪比、 均方误差、峰值相对误差、峰位误差和相位误差等方面都有一定程度的改善. 关键词： 脉冲星信号消噪 经验模态分解 噪声模态单元预判 局部均方误差     

X-ray Pulsar Signal Denoising Based on Variational Mode Decomposition

Pulsars, especially X-ray pulsars detectable for small-size detectors, are highly accurate natural clocks suggesting potential applications such as interplanetary navigation control. Due to various complex cosmic background noise, the original pulsar signals, namely photon sequences, observed by detectors have low signal-to-noise ratios (SNRs) that obstruct the practical uses. This paper presents the pulsar denoising strategy developed based on the variational mode decomposition (VMD) approach. It is actually the initial work of our interplanetary navigation control research. The original pulsar signals are decomposed into intrinsic mode functions (IMFs) via VMD, by which the Gaussian noise contaminating the pulsar signals can be attenuated because of the filtering effect during signal decomposition and reconstruction. Comparison experiments based on both simulation and HEASARC-archived X-ray pulsar signals are carried out to validate the effectiveness of the proposed pulsar denoising strategy.     

Application of Hilbert–Huang transform to laser Doppler velocimeter

A new method based on Hilbert–Huang transform is proposed to analyze the laser Doppler signal with a large acceleration. The Doppler signal is decomposed into several Intrinsic Mode Functions (IMFs) via empirical mode decomposition (EMD). And the Hilbert transform is used to compute the instantaneous frequency. The vehicle velocity parameter is estimated by taking linear fitting on the instantaneous frequency of the relevant IMF. The simulation results show that the HHT-based method is quite useful for the LDV that offers velocity parameter to the vehicle self-contained navigation system when the vehicle moves at a large acceleration.     

Outboard abnormal noise source localization method with curved surface projection based on time delay matching and weighting criterion

An improved localization method consisting of "filtering-time delay estimationhyperbolic localization" is proposed. Combining the empirical mode decomposition(EMD)and time delay estimation method based on generalized average magnitude difference function,the original signals are decomposed into intrinsic mode function(IMF) components. The energy distribution criterion and spectrum consistency criterion are used to select the IMFs, which can represent the physical characteristics of the source signal. Several sets of signals are applied to estimate the time delay, and then a vector matching criterion is proposed to select the correct time delay estimation. Considering the hydrophones location, a shell model is established and projected to a plane according to the quadrant before the hyperbolic localization. Results of mooring and sailing tests show that the proposed method improves the localization accuracy,and reduces the error caused by time delay estimation.     

基于小波域可导阈值函数与自适应阈值的脉冲星信号消噪

脉冲星辐射信号具有极低的信噪比, 传统降噪方法难以在抑制噪声的同时保留其细节信息. 为此, 提出了一种小波域脉冲星信号消噪方法. 在小波域, 利用一种可导的阈值函数和一种自适应阈值选取方法, 对含噪脉冲星信号进行小波域阈值去噪处理, 并利用信噪比(SNR)、 均方根误差(RMSE)、 峰值相对误差(REPV) 以及峰位误差(EPP) 四项指标来对去噪效果进行评价. 实验结果表明, 与软阈值与硬阈值法相比, 该方法能在有效去除含噪脉冲星信号中的噪声、 显著提高其信噪比的同时, 更有效地保留原始信号中的有用信息, 同时可以获得更小的均方根误差、 脉冲峰值相对误差与峰位误差.     

总体经验模态分解能量向量用于ECG能量分布的研究

总体经验模态分解(EEMD)改进了经验模态分解(EMD)存在的模态混叠问题, 依据信号自身的波动特点将信号分解, 特别适合非线性非平稳信号的分析处理. ECG信号能量分布有一定的规律, 疾病会引起能量分布的变化, 研究ECG能量分布的改变对心脏疾病的研究和临床诊断有重要意义. 本文将ECG信号通过EEMD方法分解为多个本征模态函数(IMF)分量, 观察IMF分量的波动规律, 指出了ECG信号在不同时间尺度上的波动特点和物理意义. 将IMF分量分别计算能量, 得到ECG的能量向量, 并对健康人和三种心脏疾病患者能量向量进行对比分析. 结果表明心脏疾病导致EEMD能量向量的高频分量显著降低, 尤其是p₁分量具有较好的区分度, 可以作为心脏疾病诊断的参考依据. 相比较传统的频域分析方法单纯关注频率而忽略信号自身特点和信号成分之间的相互作用, EEMD的分解结果依赖于ECG信号本身, 因此更能够反映ECG信号的真实情况, 揭示年龄和疾病对ECG能量分布的影响.     

Studies of spectral properties of short genes using the wavelet subspace Hilbert–Huang transform (WSHHT)

This paper presents a new algorithm for the analysis of spectral properties of short genes using the wavelet transform and the Hilbert–Huang transform (HHT). A wavelet subspace algorithm combined with the empirical mode decomposition (EMD) is introduced to create subdivided intrinsic mode functions (IMFs) and a cross-correlation analysis is applied to remove pseudo-spectral components. Experiments are carried out on DNA sequences with the double-base (DB) curve representation and the results show that the signal-to-noise ratio of buried signals can be enhanced using the proposed method, yielding significant patterns that are rarely observed with conventional methods. The wavelet subspace Hilbert–Huang transform (WSHHT) algorithm is able to correctly identify spectral patterns of very short genes (below 70 bp) in DNA sequences.     

基于Curvelet变换的软硬阈值折衷图像去噪

与小波变换相比,Curvelet变换更好地表达图像的边缘和细节,因此更适合多尺度图像去噪。针对软阈值和硬阈值去噪方法存在的不足,提出了基于Curvelet变换域的软硬阈值折衷去噪法,并采用不同的阈值自适应地对不同的Curvelet子带进行阈值化。实验结果表明该方法对图像中的边缘、弱的直线和曲线特征有更好的恢复。去噪后图像PSNR值更高,视觉效果更好。     

Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect

Gears are one of the most common and important machine components in many advanced machines. An improved understanding of vibration signal is required for the early detection of incipient gear failure to achieve high reliability. This paper mainly consists of two parts: in the first part, a 6-degree-of-freedom gear dynamic model including localized tooth defect has been developed. The model consists of a spur gear pair, two shafts, two inertias representing load and prime mover and bearings. The model incorporates the effects of time-varying mesh stiffness and damping, backlash, excitation due to gear errors and profile modifications. The second part consists of signal processing of simulated and experimental signals. Empirical mode decomposition (EMD) is a method of breaking down a signal without leaving a time domain. The process is useful for analysing non-stationary and nonlinear signals. EMD decomposes a signal into some individual, nearly monocomponent signals, named as intrinsic mode function (IMF). Crest factor and kurtosis have been calculated of these IMFs. EMD pre-processed kurtosis and crest factor give early detection of pitting as compared to raw signal.     

Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes

The 1D empirical mode decomposition method is applied to reduce speckle noise in the correlation fringes produced in digital speckle pattern interferometry. This method is based on the decomposition of a signal in a sum of well-behaved fast and slow oscillation modes through a sifting process, which generates a fully data-driven technique. Consequently, this is an adaptive approach and the use of basis functions in the analysis process is not required. The denoised signal is given by the residue obtained after the fast oscillation modes are removed. The performance and limitations of the denoising technique are analyzed using computer simulated fringes and these results are compared with those obtained using a wavelet sub-band removal approach. An application of the EMD method to denoise experimental correlation fringes is also presented.