Statistical pulse compression

The seismic method in petroleum exploration is an echo-location technique to detect interfaces between the subsurface sedimentary layers of the earth. The received seismic reflection record (field trace), in general, may be modeled as a linear time-varying (LTV) system. However, in order to make the problem tractable, we do not deal with the entire field trace as a single unit, but instead subdivide it into time gates. For any time gate on the trace, there is a corresponding vertical section of rock layers within the earth, such that the primary (direct) reflections from these layers all arrive within the gate. Each interface between layers is characterized by a local (or Fresnel) reflection coefficient, which physically must be less than unity in magnitude. Under the hypothesis that the vertical earth section has small reflection coefficients, then within the corresponding time gate the LTV model of the seismic field trace reduces to a linear time-invariant (LTI) system. This LTI system, known as the convolutional model of the seismic trace, says that the field trace is the convolution of a seismic wavelet with the reflection coefficient series. If, in addition, the reflection coefficient series is white, then all the spectral shape of the trace within the gate can be attributed to the seismic wavelet. Thus the inverse wavelet can be computed as the prediction error operator (for unit prediction distance) by the method of least squares. The convolution of this inverse wavelet with the field trace yields the desired reflection coefficients. This statistical pulse compression method, known as predictive deconvolution with unit prediction distance, is also called spike deconvolution. Alternatively, predictive deconvolution with greater prediction distance can be used, and it is known as gapped deconvolution. Other pulse compression methods used in seismic processing are signature deconvolution, wavelet processing, and minimum entropy deconvolution.     

Simultaneous wavelet estimation and deconvolution of reflectionseismic signals

The problem of simultaneous wavelet estimation and deconvolution is investigated with a Bayesian approach under the assumption that the reflectivity obeys a Bernoulli-Gaussian distribution. Unknown quantities, including the seismic wavelet, the reflection sequence, and the statistical parameters of reflection sequence and noise are all treated as realizations of random variables endowed with suitable prior distributions. Instead of deterministic procedures that can be quite computationally burdensome, a simple Monte Carlo method, called Gibbs sampler, is employed to produce random samples iteratively from the joint posterior distribution of the unknowns. Modifications are made in the Gibbs sampler to overcome the ambiguity problems inherent in seismic deconvolution. Simple averages of the random samples are used to approximate the minimum mean-squared error (MMSE) estimates of the unknowns. Numerical examples are given to demonstrate the performance of the method     

An algorithm for successive identification of reflections

A new algorithm for successive identification of seismic reflections is proposed. Generally, the algorithm can be viewed as a curve matching method for images with specific structure. However, in the paper, the algorithm works on seismic signals assembled to constitute an image in which the investigated reflections produce curves. In numerical examples, the authors work on signals assembled in CMP gathers. The key idea of the algorithm is to estimate the reflection curve parameters and the reflection coefficients along these curves by combining the multipulse technique and the generalized Radon transform. The multipulse technique is used for wavelet identification in each trace, and the generalized Radon transform is used to coordinate the wavelet identification between the individual traces. Furthermore, a stop criterion and a reflection validation procedure are presented. The stop criterion stops the reflection estimation when the actual estimated reflection is insignificant. The reflection validation procedure ensures that the estimated reflections follow the shape of the investigated reflection curves. The algorithm is successfully used in two numerical examples. One is based on a synthetic CMP gather, whereas the other is based on a real recorded CMP gather. Initially, the algorithm requires an estimate of the wavelet that can be performed by any wavelet estimation method.     

应用小波变换和双谱方法实现弱信号检测

为提高微弱信号检测概率,提出了一种应用小波变换和双谱分析的方法。利用小波变换减少大部分随机噪声,提高信噪比,再进行双谱分析,获得比功率谱更丰富的信息,抑制高斯噪声,提高检测概率。通过模型计算和验证,证明了该方法的可行性和有效性。     

基于双通道检测的多比特盲水印最优检测器的设计

水印检测错误会严重损害水印系统的可信度。该文提出基于双谱和能量检测的双通道检测来实现最优盲水印检测器的设计,并给出了一种在小波域中的具体实现。传统检测方法检测概率会随着信噪比的下降而急剧下降。双通道检测时信噪比很小时只要有足够大的双谱信息,即可得到较高的检测概率。即使双谱信息很小时双通道检测系统退化为似然比检测系统,仍是最优的。检测器检测到指定的水印后利用独立分量分析技术进行水印盲恢复。实验过程中攻击由通用水印测试软件Stirmark产生,实验数据证明所设计的最优盲检测器对Stirmark提供的各种攻击(如剪切、JPEG压缩、删行/列、旋转、尺度变换、随机几何攻击等)具有很好的鲁棒性。实验结果说明这种最优检测器的性能优越于现有的水印检测器。     

Inversion of band-limited reflection seismograms: Theory and practice

This paper examines the problem of recovering the acoustic impedance from band-limited normal incidence reflection seismograms. Recognizing the inherent nonuniqueness in the inversion, we proceed by constructing an impedance model which satisfies the processed seismogram, has a minimum of structural variation, honors any point impedance constraints that are provided, and incorporates information from stacking velocities. The constrained inversion is carried out in a single operation using linear programming methods. The constructed impedance is consistent with available geological and geophysical information and therefore constitutes a well-constrained estimate of the true earth impedance. A basic assumption in our inversion is that each seismic trace is a band-limited representation of the true reflectivity function. When seismic data do not conform with this assumption, pre-inversion processing of the data is required; this involves a series of data checks and possible corrections. A complete processing sequence incorporating all steps of the practical inversion is presented and illustrated with field data examples.     

AR model order selection based on bispectral cross correlation

A novel method is presented for optimal model order selection for autoregressive (AR) bispectrum estimation. The method depends solely on the data and requires no a priori information about the process. The method selects the model order that maximizes the cross correlation between the direct (fast Fourier transform-based) bispectrum estimate and the autoregressive bispectrum estimate. Simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise     

Maximum-Likelihood Seismic Deconvolution

The purpose of this paper is to describe a broad spectrum of seismic deconvolution problems and solutions which we refer to collectively as maximum-likelihood (seismic) deconvolution (MLD). Our objective is to perform deconvolution and wavelet estimation for the case of nonminimum phase wavelets. Our approach is to exploit state-variable technology, maximum-likelihood estimation, and a sparse spike train (Bernoulli-Gaussian) model for the reflection signal. Our solution requires detection of significant reflectors, wavelet and variance identification (nonlinear optimization), and estimation of the spike density parameter.     

Bispectrum estimation: A digital signal processing framework

It is the purpose of this tutorial paper to place bispectrum estimation in a digital signal processing framework in order to aid engineers in grasping the utility of the available bispectrum estimation techniques, to discuss application problems that can directly benefit from the use of the bispectrum, and to motivate research in this area. Three general reasons are behind the use of bispectrum in signal processing and are addressed in the paper: to extract information due to deviations from normality, to estimate the phase of parametric signals, and to detect and characterize the properties of nonlinear mechanisms that generate time series.     

Wavelet estimation

An important problem in seismic exploration is the estimation of and correction for the seismic wavelet. A seismic signal may be modeled as a convolutional model with the wavelet as one component. The wavelet propagated by the seismic energy source is complicated by transmission and recording filters. Some filters in the system can be deterministically defined while others are more conjectural. The estimation of the wavelet is useful in two major ways. Borehole measurements are used to model the surface seismograms. The wavelet used in the model needs to match that of the seismogram to correlate the two measurements. Conversely, the estimated wavelet can be used to design inverse filters which make the seismogram approach the borehole measures. Some well-known methods for estimation of the wavelet are based on assumptions about the wavelet or the earth reflectivity. Examples of the methods indicate success on some data even though each makes different assumptions. The methods serve to point out basic problems in reliably estimating the wavelet from the seismogram. Basic problems include noise, band-limiting, nonstationarity, uncertain theoretical models, assumption failure, and widely diverse geological sequences of the earth. Quality control or evaluation of the performance of an estimation algorithm is a nontrivial problem. The estimation of the wavelet from a seismic recording remains an area of challenging research and importance in exploration for hydrocarbons.     

超宽带雷达信号处理技术和实验研究

针对探测空中目标的超宽带(UWB)/冲激雷达,本文讨论了UWB/冲激雷达的信号处理技术,主要是信号检测和目标特性分析,首先讨论了目标检测技术,提出了用小波变换和高阶谱估计技术在变换域内进行检测的算法;其次讨论了目标特性分析技术,采用了高阶谱估计,提出了一种时域双谱估计算法,它可精确估计复杂形体目标的局部散射中心的分布.最后,结合作者等人研制的冲激雷达实验系统,对上述信号处理方法进行了实验研究,验证了上述信号处理方法的有效性。     

Simultaneous Spherical Divergence Correction and Optima Deconvolution

The effects of spherical divergence on reflection seismograms destroys the stationarity assumption implicit in Weiner smoothing by distorting the amplitudes of the reflection coefficient sequence. The traditional correction for spherical divergence consists of an immediate scaling of the observed signal by an expected attenuation factor. It is this correction that violates the stationarity assumption, for it distorts the amplitudes of the observation noise process. Attempts to adapt the Weiner smoother to time-varying signals by time gating are cumbersome and suboptimal. In this paper, we show how to implement a Kalman deconvolution smoother which compensates for the effects of spherical divergence. The implementation is simple and straightforward, and estimates of the reflection coefficient sequence are optimal and corrected in amplitude. A computational example which compares our approach to an ad hoc Weiner smoother is provided for a simulated seismic signal. By means of this example, we demonstrate better performance for our approach over the Weiner smoother approach.     

一种新的雷达辐射源信号识别方法研究

随着雷达技术的发展,雷达体制的多样性和雷达信号的复杂性对雷达辐射源信号识别技术提出了严峻的挑战。循环双谱抗噪性能强,且包含了丰富的信息,能用于识别雷达辐射源信号。但是其数据量庞大,而循环双谱对角切片法丢失了大部分信息。证明了循环双谱的对称性和周期性,提出了局部轴向积分循环双谱。该方法首先计算信号的循环双谱,然后在两个谱频率构成的平面上沿平行于谱频率轴的直线积分,最后用Fisher判决率（FDR）选择鉴别能力较强的轴向积分循环双谱。这样不但能有效地减小数据量,而且保留了大部分有用的循环双谱信息。仿真条件下,对比分析了局部轴向积分循环双谱与循环双谱对角切片的识别效果,结果表明新方法的识别率远远优于循环双谱对角切片法。      

On the robust control of nonlinear systems

In this paper we consider robust stabilization of the class of nonlinear plants of the form $$\dot x = f(x) + \sum\limits_{i = 1}^m {g_i } (x)u_i (t),$$ which are equivalent, under smooth state space coordinate transformations and nonlinear state feedback, to controllable systems. This approach is very sensitive for unknown parameters' values. Parameter adaptation may be used as a technique to robustify minimum-phase systems [3]. We give an example of a locally stable adaptive tracking system in which the last assumption is weakened. The minimum-phase plant considered in the paper is a current-controlled squirrel cage induction motor.     

Ultrawide band radar signal detection, estimation and experiment

With reference to the air target detection of ultra-wide band (UWB)/impulse radar(IR), the transient signal processing techniques was discussed. In weak UWB signal detection, the wavelet transforms and high order spectrum estimation techniques were preferred. In target characteristic analysis, a time domain bispectrum estimation algorithm was used to analyze the target impulse response, which could estimate accurately local scattering distribution of complex target. A free field IR experimental system installed in an anechoic chamber was used. With this system, experiments to several target models were made. The results of these experiments verified the signal processing method efficiency.     

Bispectrum estimation via AR modeling

The bispectrum of process is a quantity that provides information about quadratic phase coupling of its harminic components and also deviation from normality. This information is essentially contained in its third moment sequence. In this paper a new method that provides a bispectrum estimate in terms of the frequency response of an autoregressive (AR) filter is presented. The parameters of the filter try to approximate the third moments of the underlying process. This method is shown to provide much higher resolution than existing conventional methods for bispectrum estimation and is especially suitable for short length data.     

基于小波变换域的参数化双谱心音信号分析方法的研究

本文利用心音信号在小波域的分布特点,提出了一种基于小波变换域的参数化双谱心音信号分析方法。通过对不同类别的心音信号数据分析表明,本方法不仅能抑制各类噪声的干扰,而且能有效地区分不同情绪状态下心音信号的模式特征,为分析人类情绪变化的特点提供了一种实用而有效的方法。     

Multiscale signal enhancement: beyond the normality andindependence assumption

Current approaches to denoising or signal enhancement in a wavelet-based framework have generally relied on the assumption of normally distributed perturbations. In practice, this assumption is often violated and sometimes prior information of the probability distribution of a noise process is not even available. To relax this assumption, we propose a novel nonlinear filtering technique in this paper. The key idea is to project a noisy signal onto a wavelet domain and to suppress wavelet coefficients by a mask derived from curvature extrema in its scale space representation. For a piecewise smooth signal, it can be shown that filtering by this curvature mask is equivalent to preserving the signal pointwise Holder exponents at the singular points and lifting its smoothness elsewhere.     

基于双谱特征的超宽带雷达人体目标识别

为了在人体微多普勒特征不明显条件下识别静态人体目标及人体姿态,提出了一种结合双谱对角线起伏特性与目标强散射点分布特征进行人体目标识别的方法。首先,通过分析静态人体目标双谱,提取双谱对角线起伏特性作为分类特征,降低了双谱数据的维数,减少了双谱特征冗余。然后,结合目标强散射点分布特征从不同角度描述目标,并构造用于目标识别的特征向量。最后,用支持向量机实现目标识别。仿真和实测结果均表明,双谱对角线起伏特性与目标强散射点分布特征融合的方法可以有效识别出静态人体目标并且实现人体姿态识别。     

Bispectral analysis and reconstruction in the frequency domain of mono- and bidimensional deterministic sampled signals

Deterministic sampled signals bispectra are periodic and hold more information than analog signal bispectra. After showing this difference, the communication presents two algorithms for reconstructing a sampled signal Fourier transform from its bispectrum: the first is a least squares reconstruction method deducing the Fourier transform logarithm from the bispectrum logarithm through a simple average; the second is an algorithm for reconstructing the Fourier transform from a restricted number of values on the bispectrum diagonal slice by a simple resolution of linear equations. The resistance of both algorithms to the measurement noise is given.