基于尺度间和尺度内相关陛的平稳小波红外图像去噪

提出了一种基于尺度间和尺度内相关性的平稳小波变换红外图像去噪方法。首先对红外图像进行离散平稳小波变换,分别对各个分解层的高频子带,利用不同尺度小波系数形成的系数向量,通过线性最小均方误差估计小波系数,获得各个高频子带的估计系数,再利用小波系数尺度内的邻域相关性对小波系数进行修正,然后通过小波反变换得到去噪图像。仿真结果表明,考虑尺度间和尺度内相关性的平稳小波红外图像去噪算法能有效地去除红外图像噪声,在信噪比和视觉质量上要优于单纯考虑尺度间相关性的去噪方法。     

基于尺度间和尺度内相关性的平稳小波红外图像去噪

提出了一种基于尺度间和尺度内相关性的平稳小波变换红外图像去噪方法.首先对红外图像进行离散平稳小波变换,分别对各个分解层的高频子带,利用不同尺度小波系数形成的系数向量,通过线性最小均方误差估计小波系数,获得各个高频子带的估计系数,再利用小波系数尺度内的邻域相关性对小波系数进行修正,然后通过小波反变换得到去噪图像.仿真结果表明,考虑尺度间和尺度内相关性的平稳小波红外图像去噪算法能有效地去除红外图像噪声,在信噪比和视觉质量上要优于单纯考虑尺度间相关性的去噪方法.     

基于小波局部统计特性的图像去噪方法

本文提出一种利用图像在小波域上局部统计特性的自适应去噪方法。首先在LMMSE准则下,推导出小波系数在局部区域的恢复公式。为进一步精确地估计理想小波系数的局部方差,本算法提出利用尺度间和子带内的相关性,即利用粗尺度下小波系数的局部方差预测精细尺度下相应位置的小波系数为噪声成分的概率,以及常规估计下的小波系数的局部方差是否小于某个门限值判断其是否为噪声成分。然后以这些局域窗内非噪声成分系数估计理想小波系数局部方差。实验结果表明,本算法与传统算法相比,对图像质量有进一步地改善,尤其是对细节丰富的图像表现地更为突出。     

间歇混沌合成1/f噪声的相关特性分析

本文利用非线性随机微分方程来合成间歇混沌信号,针对该信号表现出的1/f噪声特征,在不同消失矩的小波基下进行相关特性分析.仿真结果发现,在功率谱的中间频段内,该信号的功率谱密度表现出典型的1/f噪声特性,其小波变换系数方差与相应的小波尺度呈对数线性关系;且在该频段内,部分尺度下该间歇性信号的小波变换系数的相关性随小波基的消失矩的增大而减小,在另一部分尺度下该相关性则随着消失矩的增大而增大.实验结果表明,随小波消失矩的增大,并非在所有尺度下小波变换对该间歇性信号均具有去相关作用.论文讨论了小波变换系数的方差和尺度的关系,详细分析了小波变换系数的相关性随小波消失矩的变化趋势.     

1/f类分形信号的最小二乘法参数估计

根据含噪1/f类分形信号的小波变换系数方差随尺度变化的特点,该文提出了一种估计1/f类分形信号参数的新方法,即对其小波系数方差进行简单的变换,使1/f类分形信号参数估计满足最小二乘法参数估计的条件。仿真实验结果表明,该方法可以有效地从加性白噪声背景下估计出1/f类分形信号的,2等参数,从而使1/f类分形信号与加性白噪声分离。     

估计小波系数方差邻域大小的研究

利用小波变换去噪时小波系数方差的估计对去噪结果影响很大。自然图像小波分解后得到的系数在不同的分辨率中差异很大,所以利用邻域估计中心点方差时,不同分辨率应有不同大小的邻域。首先对在邻域中利用极大似然准则估计中心点方差进行分析,再结合自然图像小波分解后的系数在不同分辨率子带中,根据平稳性和重要性选择邻域的大小。最后进行去噪实验,并取得正交小波分解下理想的去噪性能。     

非平稳分形随机信号波形估计的最优门限方法

本文用基于最小均方误差准则的最优门限方法估计叠加高斯白噪声的分形布朗运动,并给出其离散小波变换分解级数确定方法.与多尺度维纳滤波相比,本方法不需估计1/f类分形信号的方差,且其离散小波变换分解级数可预先确定,因此有着更好的实用性和可操作性.     

基于多尺度分析的混沌态Boost电路的分形研究

分形维数是混沌吸引子的重要特征参数,而小波变换是一种多尺度分析工具。该文研究了混沌信号的自相似性及其不同尺度小波变换系数的特性,推导出计算混沌信号分形维数的多尺度计算方法,并对Boost电路混沌信号的分形维数进行了仿真计算,清楚刻画了其混沌吸引子的分形特性。     

一种小波系数模型在图像噪声参数估计中的应用

在小波图像处理中,通常利用HH子带来估计高斯白噪声方差,目前流行的估计方法是由Donoho和Johnstone提出的(简称DJ法),但是该方法给出的估计值通常都偏大。针对这一点,该文将他们的方法结合双随机小波系数模型,提出了一种新的、递归的方差估计方法。在已由Donoho的方法获得噪声方差估计的粗略估计的情况下,新方法利用统计学理论将HH子带中的信号滤除从而得到更接近于纯噪声的HH子带,然后利用这一新的HH子带来估计噪声的方差。结合EM参数估计方法,该方法还可以实现非高斯噪声参数的估计,实验表明新方法同Donoho法相比有很大的改善。     

光纤陀螺随机误差特性的小波方差分析

光纤陀螺各项随机误差的频率特性各不相同.小波变换的多分辨分析兼具时频分析和尺度分析的功能,故采用小波方差法来表征噪声在不同频率分量的变化情况,从而为特定环境下光纤陀螺的故障诊断以及误差分析提供参考.通过与传统的分析光纤陀螺随机误差特性的Allan方差法对比可知,只要小波基函数的支撑区间足够小,小波方差就能克服Allan方差能量泄露的缺点.利用60Co辐照源模拟空间辐照,进行光纤陀螺整机辐照实验,分析实验数据,证明小波方差比Allan方差能够更加精确地反映光纤陀螺各项随机误差的变化情况.     

Asymptotic decorrelation of between-Scale Wavelet coefficients

In recent years there has been much interest in the analysis of time series using a discrete wavelet transform (DWT) based upon a Daubechies wavelet filter. Part of this interest has been sparked by the fact that the DWT approximately decorrelates certain stochastic processes, including stationary fractionally differenced (FD) processes with long memory characteristics and certain nonstationary processes such as fractional Brownian motion. It is shown that, as the width of the wavelet filter used to form the DWT increases, the covariance between wavelet coefficients associated with different scales decreases to zero for a wide class of stochastic processes. These processes are Gaussian with a spectral density function (SDF) that is the product of the SDF for a (not necessarily stationary) FD process multiplied by any bounded function that can serve as an SDF on its own. We demonstrate that this asymptotic theory provides a reasonable approximation to the between-scale covariance properties of wavelet coefficients based upon filter widths in common use. Our main result is one important piece of an overall strategy for establishing asymptotic results for certain wavelet-based statistics.     

自相似业务流HURST参数小波检测法的研究

本文介绍了小波对自相似业务流Hurst参数的检测原理。重点分析了消失矩,分解级数对检测结果的影响,提出了一种由品质因数确定分解级数选择的方法,给出了小波法检测的适用范围,即小波法只适用于严格重尾分布的业务源, 而不适用于非严格重尾分布的业务源,并通过仿真对结论进行了验证。     

Wavelet spectrum and its characterization property for randomprocesses

The wavelet spectrum of a random process comprises the variances of the wavelet coefficients of the process computed within each scale. This paper investigates the possibility of using the wavelet spectrum, obtained from a continuous wavelet transform (CWT), to uniquely represent the second-order statistical properties of random processes-particularly, stationary processes and long-memory nonstationary processes. As is well known, the Fourier spectrum of a stationary process is mathematically equivalent to the autocovariance function (ACF) and thus uniquely determines the second-order statistics of the process. This characterization property is shown to be possessed also by the wavelet spectrum under very mild regularity conditions that are easily satisfied by many widely used wavelets. It is also shown that under suitable regularity conditions, the characterization property remains valid for processes with stationary increments including 1/f noise     

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.     

激光陀螺信号的小波滤波方法研究

随机噪声是影响激光陀螺精度的一个重要因素,其中随机噪声包括分形噪声和白噪声,采用传统的方法很难去除分形噪声.对于激光陀螺中的随机噪声,利用分形噪声在小波变换域的特殊性质采用小波变换域参数估计方法获得噪声参数;然后采用小波阈值滤波方法去除噪声.对某型号的激光陀螺的滤波结果表明了该方法的有效性.     

Fault detection and isolation using concatenated wavelet transform variances and discriminant analysis

A method for fault detection and isolation is developed using the concatenated variances of the continuous wavelet transform (CWT) of plant outputs. These concatenated variances are projected onto the principal component space corresponding to the covariance matrix of the concatenated variances. Fisher and quadratic discriminant analyses are then performed in this space to classify the concatenated sample CWT variances of outputs in a given time window. The sample variance is a variance estimator obtained by taking the displacement average of the squared wavelet transforms of the current outputs. This method provides an alternative to the multimodel approach used for fault detection and identification, especially when system inputs are unmeasured stochastic processes, as is assumed in the case of the mechanical system example. The performance of the method is assessed using matrices having the percentage of correct condition identification in the diagonal and the percentages misclassified conditions in the off-diagonal elements. Considerable performance improvements may be obtained due to concatenation-when two or more outputs are available-and to discriminant analysis, as compared with other wavelet variance methods.     

Wavelet representations of stochastic processes and multiresolutionstochastic models

Deterministic signal analysis in a multiresolution framework through the use of wavelets has been extensively studied very successfully in recent years. In the context of stochastic processes, the use of wavelet bases has not yet been fully investigated. We use compactly supported wavelets to obtain multiresolution representations of stochastic processes with paths in L² defined in the time domain. We derive the correlation structure of the discrete wavelet coefficients of a stochastic process and give new results on how and when to obtain strong decay in correlation along time as well as across scales. We study the relation between the wavelet representation of a stochastic process and multiresolution stochastic models on trees proposed by Basseville et al. (see IEEE Trans. Inform. Theory, vol.38, p.766-784, Mar. 1992). We propose multiresolution stochastic models of the discrete wavelet coefficients as approximations to the original time process. These models are simple due to the strong decorrelation of the wavelet transform. Experiments show that these models significantly improve the approximation in comparison with the often used assumption that the wavelet coefficients are completely uncorrelated     

Estimation of 2-D noisy fractional Brownian motion and itsapplications using wavelets

The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorithms for 2-D isotropic fBm images are simple extensions of the one-dimensional (1-D) fBm estimation method. This method does not perform well when the image size is small (say, 32x32). We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coefficients across scales. Our method places no restriction on the wavelets. Also, it provides a robust parameter estimation for small noisy fractal images. For image denoising, a Wiener filter is constructed by our algorithm using the estimated parameters and is then applied to the noisy wavelet coefficients at each scale. We show that the averaged power spectrum of the denoised image is isotropic and is a nearly 1/f process. The performance of our algorithm is shown by numerical simulation for both the fractal parameter and the image estimation. Applications to coastline detection and texture segmentation in a noisy environment are also demonstrated.     

Using wavelet transform and fuzzy neural network for VPC detection from the Holter ECG

A novel method for detecting ventricular premature contraction (VPC) from the Holter system is proposed using wavelet transform (WT) and fuzzy neural network (FNN). The basic ideal and major advantage of this method is to reuse information that is used during QRS detection, a necessary step for most ECG classification algorithm, for VPC detection. To reduce the influence of different artifacts, the filter bank property of quadratic spline WT is explored. The QRS duration in scale three and the area under the QRS complex in scale four are selected as the characteristic features. It is found that the R wave amplitude has a marked influence on the computation of proposed characteristic features. Thus, it is necessary to normalize these features. This normalization process can reduce the effect of alternating R wave amplitude and achieve reliable VPC detection. After normalization and excluding the left bundle branch block beats, the accuracies for VPC classification using FNN is 99.79%. Features that are extracted using quadratic spline wavelet were used successfully by previous investigators for QRS detection. In this study, using the same wavelet, it is demonstrated that the proposed feature extraction method from different WT scales can effectively eliminate the influence of high and low-frequency noise and achieve reliable VPC classification. The two primary advantages of using same wavelet for QRS detection and VPC classification are less computation and less complexity during actual implementation.