Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

A technique to improve the empirical mode decomposition in the Hilbert-Huang transform

The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a sys- tem.To admit well-behaved Hilbert transforms,component decomposition of signals must be performed beforehand.This was first systematically implemented by the empirical mode decomposition(EMD)in the Hilbert-Huang transform,which can provide a time-frequency representation of the signals.The EMD,however,has limitations in distinguishing different components in narrowband signals commonly found in free-decay vibration signals.In this study,a technique for decompo- sing components in narrowband signals based on waves' beating phenomena is proposed to improve the EMD,in which the time scale structure of the signal is unveiled by the Hilbert transform as a result of wave beating,the order of component ex- traction is reversed from that in the EMD and the end effect is confined.The proposed technique is verified by performing the component decomposition of a simulated signal and a free decay signal actually measured in an instrumented bridge structure.In addition,the adaptability of the technique to time-variant dynamic systems is demonstrated with a simulated time-variant MDOF system.

Study of seismic spectrum decomposition based on CEEMD

Empirical mode decomposition( EMD) is a powerful tool of time-frequency analysis. EMD decomposes a signal into a series of sub-signals,called Intrinsic mode functions( IMFs). Each IMF contains different frequency components which can deal with the nonlinear and non-stationary of signal. Complete ensemble empirical mode decomposition( CEEMD) is an improved algorithm,which can provide an accurate reconstruction of the original signal and better spectral separation of the modes. The authors studied the decomposition result of a synthetic signal obtained from EMD and CEEMD. The result shows that the CEEMD has suitability in spectrum decomposition time-frequency analysis. Compared with traditional methods,a higher time-frequency resolution is obtained through verifying the method on both synthetic and real data.

Segmented second algorithm of empirical mode decomposition

A new algorithm, named segmented second empirical mode decomposition （EMD） algorithm, is proposed in this paper in order to reduce the computing time of EMD and make EMD algorithm available to online time-frequency analysis. The original data is divided into some segments with the same length. Each segment data is processed based on the principle of the first-level EMD decomposition. The algorithm is compared with the traditional EMD and results show that it is more useful and effective for analyzing nonlinear and non-stationary signals.

Simulation Study on Multi-Rate Time-Frequency Analysis of Non-Stationary Signals

A new time-frequency analysis method is proposed in this study using a multi-rate signal decomposition technique for the analysis of non-stationary signals. The method uses a multi-rate filter bank for an improved non-stationary signal decomposition treatment, and uses the Wigner-Ville distribution(WVD) analysis for signal reconstruction. The method presented in this study can effectively resolves the time and frequency resolution issue for non-stationary signal analysis and the cross-term issue typically encountered in time-frequency analysis.The feasibility and accuracy of the proposed method are evaluated and verified in a numerical simulation.

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.

Fractional S-transform-part 2:Application to reservoir prediction and fluid identification

The fractional S-transform （FRST） has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency （FRFTfr） axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.

自适应旋转投影分解法

本文提出了一种新的时一频分解方法──自适应旋转投影分解法（ＡＯＰ法）．在表征信号空间的线性调频高斯信号集上，我们针对原始信号自适应地搜索出一组与信号匹配最好的基函数序列．以此用尽可能少的基函数来重构信号子空间．根据分解系数，得到信号的时－频能量分布．由于调频高斯信号时频会聚性能极佳，又能灵活高效地匹配各类信号，该算法不论从分辨率、效率还是描述能力等方面都具有良好的性能．将它用于语音压缩也取得了很好的结果．

基于自适应定向正交投影分解的图象分割方法

将目标和背景分别对应到灰度直方图中的两个高斯分布是进行图象分割的一种常用方法 ,但复杂图象的直方图往往是多峰的 .为了更好地拟合这种复杂图象直方图的多峰特性 ,提出了一种基于自适应定向正交投影分解的图象分割方法 .该方法首先将这种复杂图象的直方图看作是多个高斯分布的叠加 ,并可通过应用自适应定向正交投影分解法来快速准确地确定每个高斯分布的权值、均值和方差 ,进而计算出各相邻高斯分布之间的最优阈值 ,以用于图象分割 .在此基础上 ,又提出了阈值分离度的概念 ,并将其作为选取最终阈值的指标 .应用实例结果表明 ,该方法能够快速有效地实现复杂图象的多阈值分割 .

基于数据融合的人脸识别方法

考虑人脸表情、光照变化和姿态对人脸识别性能的影响,提出一种基于数据融合的人脸识别方法。应用二维离散小波变换对人脸图像进行3次小波分解,使每幅人脸图像得到1幅低频子图和9幅高频子图,低频子图可以直接代表人脸的本质,而部分高频子图仍含有鉴别信息,因此,利用Fisher投影对得到的高频子图进行投影,选取出包含鉴别信息较多的高频子图,并设计3种数据融合方案。分别在数据级、特征级和决策级实现融合处理,并在ORL和YALE A人脸库上完成实验,结果表明,与主成分分析法和小波变换人脸识别方法相比,该方法能有效提高识别率。

SVD与LDA相结合的人脸特征提取方法

提出一种新的SVD与LDA相结合的人脸特征提取方法。首先选用练训样本的均值图像作为标准图像,把训练样本投影到标准图像经奇异值分解产生的基空间中,其次提取投影系数矩阵左上角信息作为初步特征,最后再采用LDA分析方法降维提取最终的特征。该方法解决了奇异值分解用于人脸识别基空间不一致的固有缺陷,同时又增加的特征的类别信息,也避免了LDA的小样本问题。在ORL与CAS-PEAL人脸库的实验结果表明了该方法的有效性,同时对光照有一定的鲁棒性。

Application of Hilbert-Huang signal processing to ultrasonic non-destructive testing of oil pipelines

In this paper, a detection technique for locating and determining the extent of defects and cracks in oil pipelines based on Hilbert-Huang time-frequency analysis is proposed. The ultrasonic signals reflected from defect-free pipelines and from pipelines with defects were processed using Hilbert-Huang transform, a recently developed signal processing technique based on direct extraction of the energy associated with the intrinsic time scales in the signal. Experimental results showed that the proposed method is feasible and can accurately and efficiently determine the location and size of defects in pipelines.

约束线性描述分析与人脸识别

针对高维、小样本模式识别中的特征提取问题,提出了一种约束线性描述分析方法(CLDA)。以线性变换后样本的类内距离与类间距离之比最小作为准则函数,同时加上约束条件使变换后的样本中心沿着特定的正交方向,通过白化变换、Gram-Schimdt正交化和正交子空间投影求解约束准则函数得到最优变换矩阵。针对人脸识别的小样本问题,根据奇异值分解定理实现白化变换。对ORL和UMIST人脸库进行了仿真研究,结果表明CLDA方法的性能接近于某些Fisher描述分析方法如直接Fisher描述分析(DDA)和改进的Fisher描述分析(R-LDA)。

加速度分解对定常约束多体系统的动力学分析

通过约束矩阵及其正交补的两组基，将定常约束多体系统的动力学方程沿与约束相容和不相容的两个方向上投影，并将系统的广义加速度沿这两个方向进行分解，得到描述系统运动的纯微分方程和求约束力的公式，同时提出了违约修正的一种方法．最后给出一个说明性例子．

快速增量主分量算法的近似协方差矩阵实现

针对主分量分析法在实际应用中运算量较大的问题,首先基于特征向量相互正交的特性,将子空间投影算法的运算量降低为原算法的1/P(P为所需的特征向量个数).然后利用大特征值及其对应的特征向量构成的近似协方差矩阵,将子空间投影算法中的广义特征值分解问题转化为特征值分解,得到运算量降低为原算法1/N(N为向量维数)的快速算法.最后基于ORL人脸数据库的实验验证了算法的有效性.

基于QR分解的扩展监督局部保留映射

针对局部保留映射(LPP)算法不能提供数据集的差异信息问题,提出一种基于QR分解的扩展有监督LPP算法。该方法对训练数据矩阵进行QR分解,采用有监督的LPP算法进行降维,利用类别信息对降维后的数据进行Fisher线性判别式分析,得到最终的映射矩阵以提高判别性能。实验结果表明,该方法较主成分分析法和LPP方法有更好的判别性能。

基于投影近似子空间跟踪算法的谐波检测方法

子空间分解类算法在理论上具有任意的高分辨率,非常适合于电力系统各类谐波的分析,但需要对高维矩阵进行特征值分解,这不仅费时而且不易于工程实现。本文将投影近似子空间跟踪算法引入电力系统谐波分析领域,详细分析评估了PASTd算法的性能。仿真结果表明,紧缩投影近似子空间跟踪算法即PASTd算法不仅保留了子空间分解类算法的超分辨率特性,而且收敛速度较快,稳定性好,可推广用于电力系统谐波检测领域。

欠定条件下同步组网跳频信号盲源分离方法

为实现欠定条件下同步组网多跳频信号的盲源分离,提出一种基于平行因子分析模型与子空间投影法的跳频信号分离方法。通过计算跳频信号时延相关矩阵构造三阶张量,将混合矩阵估计问题转化为张量CP分解问题。同时改进用于CP分解的经典最小二乘(ALS)算法,使用直接三线性分解方法粗估加载矩阵作为ALS初始迭代矩阵,在迭代过程中采用标准线搜索加速收敛得到混合矩阵。在此基础上,利用子空间投影法完成跳频信号的盲源分离,并剔除离散噪点进一步优化分离效果。仿真结果表明,该方法能够有效提高混合矩阵估计精度,改善源信号恢复效果。

基于降阶模型的中子扩散特征值问题的不确定性分析研究

为提高基于抽样统计的堆芯物理不确定性分析效率,将本征正交分解(POD)法与伽辽金(Galerkin)投影法相结合,研究了基于POD-Galerkin方法的降阶模型在堆芯物理不确定性分析中的应用可行性。以二维两群TWIGL基准题为研究对象,在各物质区群常数的有限次扰动下提取堆芯通量分布的关键变化特征,将全阶中子扩散问题在各变化特征上投影以建立降阶中子扩散模型,并以该降阶模型替代全阶模型开展物质区群常数的不确定性分析。结果表明:降阶与全阶模型计算的k eff数学期望偏差接近1 pcm,并且相比于全阶模型不确定性分析所需的计算时间,将降阶模型构造所需的全阶模型计算时间考虑在内,降阶模型的分析时间仅为其11.48%,极大地提高了不确定性分析的效率。基于拉丁超立方抽样和简单随机抽样的降阶与全阶模型计算的k eff数学期望偏差均小于8 pcm,相同样本量下拉丁超立方抽样结果的误差更小。从TWIGL基准题测试结果来看,在POD-Galerkin降阶建模中,相同样本量下,更建议采用拉丁超立方抽样方法。