用Gabo:展开进行地震数据的滤波

Gabor展开是用一组在时域及频域都局部化且具有能量集中性质的函数来展开信号,这种特征使得Gabor展开适于处理那些时间无关或非平稳的信号。利用框架理论,类似于SVD特征映像滤波方法,本文用Gabor展开滤波方法来进行地震信号的去噪处理。仿真结果显示出Gabor展开滤波方法的优越性。     

Space/spatial-frequency analysis based filtering

Space-invariant filtering of signals that overlap with noise in both space and frequency can be inefficient. However, the signal and noise may be well separated in the joint space/spatial-frequency domain. Then, it is possible to benefit from the application of space/spatial frequency approaches. Processing based on these approaches can outperform space or frequency invariant-based methods. To this aim the concept of nonstationary space-varying filtering is introduced in this paper as an extension of the time-varying filtering concept. The filtering definitions are based on statistical averages, although the filtering should commonly be applied knowing only a single noisy signal realization. The procedures that can produce good estimates of quantities crucial for efficient filtering, based on a single noisy signal realization, are considered. Special attention has been paid to the region of support estimation and cross-term effects removal. The efficiency of the proposed space/spatial-frequency filtering concept is tested on the signal forms inspired by the interferograms in optics, including real images as disturbances. Examples demonstrate the superiority of the proposed filtering over the space-invariant one for the considered type of signals and noise     

Optimal detection using bilinear time-frequency and time-scalerepresentations

Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. All existing time-frequency formulations of quadratic detection either implement classical optimal detectors equivalently in the time-frequency domain, without fully exploiting the structure of the TFR, or attempt to exploit the nonstationary structure of the signal in an ad hoc manner. We identify several important nonstationary composite hypothesis testing scenarios for which TFR/TSR-based detectors provide a “natural” framework; that is, in which TFR/TSR-based detectors are both optimal and exploit the many degrees of freedom available in the TFR/TSR. We also derive explicit expressions for the corresponding optimal TFR/TSR kernels. As practical examples, we show that the proposed TFR/TSR detectors are directly applicable to many important radar/sonar detection problems. Finally, we also derive optimal TFR/TSR-based detectors which exploit only partial information available about the nonstationary structure of the signal     

Noise reduction of image sequences using motion compensation andsignal decomposition

In this paper, a new spatio-temporal filtering method for removing noise from image sequences is proposed. This method combines the use of motion compensation and signal decomposition to account for the effects of object motion. Because of object motion, image sequences are temporally nonstationary, which requires the use of adaptive filters. By motion compensating the sequence prior to filtering, nonstationarities, i.e., parts of the signal that are momentarily not stationary, can be reduced significantly. However, since not all nonstationarities can be accounted for by motion, a motion-compensated signal still contains nonstationarities. An adaptive algorithm based on order statistics is described that decomposes the motion-compensated signal into a noise-free nonstationary part and a noisy stationary part. An RLS filter is then used to filter the noise from the stationary signal. Our new method is experimentally compared with various noise filtering approaches from literature.     

Orthonormal-basis partitioning and time-frequency representation of cardiac rhythm dynamics

Although a number of time-frequency representations have been proposed for the estimation of time-dependent spectra, the time-frequency analysis of multicomponent physiological signals, such as beat-to-beat variations of cardiac rhythm or heart rate variability (HRV), is difficult. We thus propose a simple method for 1) detecting both abrupt and slow changes in the structure of the HRV signal, 2) segmenting the nonstationary signal into the less nonstationary portions, and 3) exposing characteristic patterns of the changes in the time-frequency plane. The method, referred to as orthonormal-basis partitioning and time-frequency representation (OPTR), is validated using simulated signals and actual HRV data. Here we show that OPTR can be applied to long multicomponent ambulatory signals to obtain the signal representation along with its time-varying spectrum.     

SAR ocean image decomposition using the Gabor expansion

Demonstrates the utility of the Gabor expansion as a new tool in geophysical research. The Gabor expansion provides good time-frequency (or space-wavenumber) localization and is ideally suited to represent nonstationary processes. The properties of this tool are demonstrated by expanding an FM-chirp waveform, and azimuth cuts taken from two different SAR ocean images. The effects of filtering in Gabor phase space are also investigated     

Optimal kernels for nonstationary spectral estimation

Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by difficulties in estimation, an assumption that the signal statistics vary slowly over time. This restrictive quasistationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's (1989) class of time-frequency representations (TFR's), for estimating the Wigner-Ville spectrum of a nonstationary process. We also solve the related problem of minimum mean-squared error estimation of an arbitrary bilinear TFR of a realization of a process from a correlated observation. Both optimal time-frequency invariant and time-frequency varying kernels are derived. It is shown that in the presence of any additive independent noise, optimal performance requires a nontrivial kernel and that optimal estimation may require smoothing filters that are very different from those based on a quasistationarity assumption. Examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering     

光纤陀螺基于SNR检测的EMD滤波方法

光纤陀螺的输出信号是一种非线性、非平稳的随机信号.针对光纤陀螺信号的特点采用经验模分解(EMD)滤波法对陀螺输出信号进行滤波存在一个如何重构信号的问题,为此提出了基于信噪比检测的EMD滤波法.该方法通过连续检测相邻两个重构信号信噪比提高的程度来确定滤波后的输出信号.实验结果表明,该法能有效消除光纤陀螺信号中的噪声,并为EMD滤波法重构信号提供了一个客观的判断方法,且无需任何先验知识.     

Fetal Electrocardiogram Enhancement by Time-Sequenced Adaptive Filtering

An adaptive method for performing optimal time-varying filtering of nonstationary signals having a recurring statistical character, e.g., recurring pulses in noise, has been proposed. This method, called time-sequenced adaptive filtering, is applied to the enhancement of abdominally derived fetal electrocardiograms against background muscle noise. It is shown that substantial improvement in terms of signal distortion is obtained when time-sequenced filtering, rather than conventional time-invariant filtering, is employed. The method requires two or more abdominal channels containing correlated signal components, but uncorrelated muscle noise components. The location of the fetal pulses in time must be estimated in order to synchronize the filter's time-varying impulse response to the fetal cardiac cycle.     

B-spline signal processing. I. Theory

The use of continuous B-spline representations for signal processing applications such as interpolation, differentiation, filtering, noise reduction, and data compressions is considered. The B-spline coefficients are obtained through a linear transformation, which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering. The same property also applies for the indirect B-spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines. The filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for B-splines of any order. Applications to differentiation, filtering, smoothing, and least-squares approximation are examined. The extension of such operators for higher-dimensional signals such as digital images is considered     

Adaptive noise removal from biomedical signals using warpedpolynomials

Presents the time-warped polynomial filter (TWPF), a new interval-adaptive filter for removing stationary noise from nonstationary biomedical signals. The filter fits warped polynomials to large segments of such signals. This can be interpreted as low-pass filtering with a time-varying cutoff frequency. In optimal operation, the filter's cut-off frequency equals the local signal bandwidth. However, the author also presents an iterative filter adaptation algorithm, which does not rely on the (complicated) computation of the local bandwidth. The TWPF has some important advantages over existing adaptive noise removal techniques: it reacts immediately to changes in the signal's properties, independently of the desired noise reduction; it does not require a reference signal and can be applied to nonperiodical signals. In case of quasiperiodical signals, applying the TWPF to the individual signal periods leads to an optimal noise reduction. However, the TWPF can also be applied to intervals of fixed size, at the expense of a slightly lower noise reduction. This is the way nonquasiperiodical signals are filtered. The author presents experimental results which demonstrate the usefulness of the interval-adaptive filter in several biomedical applications: noise removal from ECG, respiratory and blood pressure signals, and base-line restoration of electroencephalograms (EEGs)     

Shear madness: new orthonormal bases and frames using chirpfunctions

The proportional-bandwidth and constant-bandwidth time-frequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tessellations of the time-frequency plane. While much effort has gone into methods for designing nice wavelet and window functions for these frameworks, little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time-frequency tilings. The authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear, or chirp, in the time-frequency plane, in addition to translate and scale. The new scale-shear fan bases and shift-shear chevron bases are obtained by operating on an existing: wavelet, Gabor (1946), or Wilson basis set with two special unitary warping transformations. In addition to the theoretical benefit of broadening the class of valid time-frequency plane tilings, these new bases could possibly also be useful for representing certain types of signals, such as chirping and dispersed signals     

Optimal quadratic detection and estimation using generalized jointsignal representations

Time-frequency analysis has significant advances in two main directions: statistically optimized methods that extend the scope of time-frequency-based techniques from merely exploratory data analysis to more quantitative application and generalized joint signal representations that extend time-frequency-based methods to a richer class of nonstationary signals. This paper fuses the two advances by developing optimal detection and estimation techniques based on generalized joint signal representations. By generalizing the statistical methods developed for time-frequency representations to arbitrary joint signal representations, this paper develops a unified theory applicable to a wide variety of problems in nonstationary statistical signal processing     

A unified approach to linear estimation problems for nonstationary processes

The linear least mean-square (LLMS) error estimation problem of a nonstationary signal corrupted by additive white noise is studied. The formulation of the problem is very general, in the sense that it deals with different estimation problems (smoothing, filtering, and prediction) involving correlation between the signal and the white noise and the possibility of estimating a linear operation (in quadratic mean) of the signal. The obtained solution is in the form of a suboptimum estimate and is derived by using the approximate series expansions for stochastic processes with the aim of solving the Wiener-Hopf equation in the general (nonstationary) case. The main characteristic of this new solution is that it can be computed efficiently using a recursive algorithm similar to the Kalman filter without requiring the signal to obey a state-space model.     

Wavelet-domain filtering for photon imaging systems

Many imaging systems rely on photon detection as the basis of image formation. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gaussian white noise, the variance of Poisson noise is proportional to the underlying signal intensity, and consequently separating signal from noise is a very difficult task. In this paper, we perform a novel gedankenexperiment to devise a new wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal and the noise, and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean-square-error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery.     

基于Gabor变换的超声回波信号时频估计

在无损检测中,超声回波往往是一个重叠较严重,含有噪声的多回波信号。根据Gabor变换时频分析的特点,该文提出一种基于Gabor变换的超声回波信号时频估计方法。该文建立回波信号与Gabor变换分析窗函数相似度(即距离)模型,通过模型相似度最小化问题转化为求解回波信号Gabor变换系数模的最大值来估计回波信号的传播时间(TOF)和中心频率(CF),最后推导它们的克拉美-罗界(CRLB)以评价算法的性能。Monte Carlo仿真和实验结果表明该文提出的算法,无论对低信噪比的单回波信号或重叠的多回波信号都能达到较高的精度,而且估计的均方误差在高信噪比时,达到CRLB,即使在低信噪比,也接近CRLB。     

离散Gabor展开及其关系

Ｇａｂｏｒ 展开是一种分析非平稳信号的工具。为了能进行数值计算,需要对连续 Ｇａｂｏｒ展开进行离散化和有限化。在过采样的一般情况下,给出了有限离散时域 Ｇａｂｏｒ 展开系数与有限离散频域 Ｇａｂｏｒ 展开系数之间的关系,并给出了一个计算实例。     

时频子空间拟合波达方向估计

本文提出了一种基于信号空时特征结构的时频子空间拟合方法,利用双线性时频分布构造时频相关矩阵 C _x代替传统的阵列相关矩阵 R _x,通过 C _x的特征分解实现了信号子空间与噪声子空间的分离.该方法在空域和二维时频域同时进行处理,能够区分具有不同时频特征的信号,既适用于平稳信号的场合又适用于时变、非平稳信号的情形,属于空时多维处理的范畴.可以证明,基于平稳信号假设的经典子空间方法是该方法的低维特例.由于包含了时变滤波的过程,因此该方法具有信号选择性以及抗干扰和抗噪声的能力.仿真结果证实了该方法的有效性.     

一种改进的自适应干扰对消技术研究及在电磁辐射测量中的应用

提出了一种适合于处理非平稳随机信号的改进自适应干扰对消算法.首先利用经验模态分解的分频特性将多频复杂信号分解到不同的固有模态函数中,再利用改进的最小均方自适应算法进行干扰对消.计算机仿真以及试验结果证明,该方法有效地滤除了含噪电磁信号中的电磁噪声干扰,提高了电磁辐射测鼍的速度和精度,具有重要的工程应用价值.