1/f分形噪声的一种多尺度Kalman滤波方法

针对淹没在1／f分形噪声中的有用信号恢复问题，提出了一种基于小波变换与Kalman滤波的多尺度滤波算法。首先将带有1／f分形噪声的信号分解成多尺度的子带信号，通过小波变换对1／f分形噪声的白化作用，消除了1／f分形噪声的自相似性和长程相关性。然后在小波域内，利用Kalman滤波实现了噪声和有用信号的分离，估计出了各子带中的有用信号。最后进行小波重构，较好地恢复出淹没在1／f分形噪声中的有用信号。仿真实验表明，使用多尺度Kalman滤波器能有效地抑制分形噪声，显著地提高了信噪比。     

基于整数小波变换的Wiener插值算法

小波变换中高低分辨率子带之间的相似性使得利用小波变换进行图像插值的方法成为可能.根据数字图像信号的特点,分析了小波变化后各个子带信号的特点,提出了基于整数小波变换的Wiener插值算法.用Wiener自适应滤波器训练得到插值滤波系数,同时结合既符合图像性质又能减小运算量的整数双正交小波基对图像插值.结果得到较高的信噪比和较好的主观视觉效果.平均峰值信噪比比传统的双线性插值法提升了2.4dB.     

小波分析在光纤陀螺分形噪声模拟中的应用

光纤陀螺随机误差的功率谱密度分别与频率的γ次方成反比,这类随机过程统称为1/fγ分形噪声,研究生成这类信号的方法对分析光纤陀螺的输出信号具有重要意义。分形噪声具有非平稳性、长程相关性、自相似性及1/fγ谱密度的特性,小波变换的多分辨分析是研究1/fγ噪声的良好工具。通过对高斯白噪声进行小波变换,再结合1/fγ噪声的方差特性,找到了满足1/fγ信号生成定理的各尺度正交小波系数,最后采用正交小波逆变换模拟出分形噪声,此方法可以产生任意噪声强度σ2、任意谱参数γ的1/fγ噪声。     

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.     

分形噪声中的信号检测

本文讨论了在1/f类分形噪声中的信号检测问题,利用小波变换对1/f噪声的近似白化作用,来消除1/f噪声间的相关性。文中给出了白化滤波器的传递函数,信号检测的判决规则和接收系统结构;分析了系统的接收性能;最后给出了仿真实验结果。     

基于多小波双变换的非线性卫星信道盲均衡算法

针对非线性卫星信道Volterra盲均衡系统收敛缓慢、计算复杂高等不足,提出了基于多小波双变换的非线性卫星信道盲均衡算法.该算法用Wiener均衡器代替Volterra均衡器,减小了均衡器结构的复杂性;用平衡正交多小波对Wiener均衡器的输入信号进行变换,降低了输入信号的自相关性;在Wiener均衡器输出端增加一级判决反馈滤波器,同时对其输入信号作平衡多小波变换,又降低了判决反馈滤波器输出信号的自相关性.仿真结果验证了该算法的有效性.     

基于小波变换的压电陀螺类噪声滤波器设计

1/fγ类随机噪声是影响压电陀螺精度的主要因素之一,其中随机信号包括白噪声和分形噪声.由于分形噪声具有长期相关性和自仿射性,采用传统的低通滤波方法难以达到有效的滤波效果.本文利用分形噪声在小波变换域的特性采用小波变换域参数估计的方法获得噪声参数,通过小波白化的方法消除分形噪声的长期相关性和自仿射性,最后应用小波软阈值的滤波方法去噪.经过对某型号压电陀螺信号进行滤波实验,结果表明这种基于小波分析的滤波方法是有效的.     

一种有效的双树复小波-Wiener滤波去噪算法

为了有效恢复被高斯白噪声污染的图像,将双树复小波变换和自适应Wiener滤波结合起来,提出了一种双树复小波-Wiener滤波去噪算法.仿真结果表明,利用该算法去噪后恢复的图像主观质量和峰值信噪比比基于正交小波变换的门限法和Wiener滤波法都要好.     

基于AR模型的小波变换在脑电信号消噪中的应用

提出了基于自回归模型(ARM)与小波变换的脑电信号分析方法,并利用他来消除脑电信号中的噪声干扰。小波变换是一种多分辨率的时间尺度分析方法,他能够将信号划分为不同频段的子带信号。根据小波变换的这一特性,对采样获得的脑电信号进行各尺度分解及消噪分析,并给出了各尺度分解结果及消噪结果。利用小波变换能有效去除脑电信号中的噪声干扰。     

一种适用于图象去噪的三通道正交完全重建滤波器组

小波变换作为一种多尺度信号分析方法,在图像处理中得到了重要的应用.图像处理的一个重要研究方向就是去噪.由于图像含有大量的边缘,因此用于图像处理的小波基必须具有良好的边缘检测性能和较强的平滑噪声能力.但是,目前还难以找到具有这样特性的正交小波基.本文利用信号的多相位表示理论,提出了一种基于Haar小波的三通道正交完全重建滤波器组,并推导出它在图像去噪中的软门限方法.试验表明,该滤波器组用于图像去噪可以得到很好的结果.     

Multiscale Wiener filter for the restoration of fractal signals:wavelet filter bank approach

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals     

Estimation of fractal signals using wavelets and filter banks

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter was recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted by external noise. The conclusions obtained in these papers are based on the following simplificative hypotheses: (1) The wavelet transformation is a whitening filter, and (2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresolution analysis is large enough. In this paper, we show that the estimation of 1/f processes in noise can be improved avoiding these two hypotheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown     

Deconvolution filter design for fractal signal transmissionsystems: a multiscale Kalman filter bank approach

A deconvolution filtering design is proposed for the 1/f fractal signal transmission systems, with its design philosophy being based on multiscale Kalman deconvolution filter bank equipped in the analysis/synthesis wavelet filter bank, The role of wavelet transformation for 1/f fractal signal process is exploited as a multiscale whitening filter for removing the properties of self-similarity and long-range dependence from the fractal signals     

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.     

基于小波变换的分形随机信号的卡尔曼滤波

本文基于多尺度卡尔曼滤波方法来估计淹没在加性高斯白噪声中的分形布朗运动.针对每一尺度,给出了相应的动态系统参数和运动模型方程以及更精确的估计算法.并与多尺度维纳滤波进行了对比,计算机仿真结果证明了其优越性.     

Optimal time-frequency deconvolution filter design fornonstationary signal transmission through a fading channel: AF filterbank approach

The purpose of this paper is to develop a new approach-time-frequency deconvolution filter-to optimally reconstruct the nonstationary (or time-varying) signals that are transmitted through a multipath fading and noisy channel. A deconvolution filter based on an ambiguity function (AF) filter bank is proposed to solve this problem via a three-stage filter bank. First, the signal is transformed via an AF analysis filter bank so that the nonstationary (or time-varying) component is removed from each subband of the signal. Then, a Wiener filter bank is developed to remove the effect of channel fading and noise to obtain the optimal estimation of the ambiguity function of the transmitted signal in the time-frequency domain. Finally, the estimated ambiguity function of the transmitted signal in each subband is sent through an AF synthesis filter bank to reconstruct the transmitted signal. In this study, the channel noise may be time-varying or nonstationary. Therefore, the optimal separation problem of multicomponent nonstationary signals is also solved by neglecting the transmission channel     

M-ary wavelet transform and formulation for perfect reconstructionin M-band filter bank

The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design     

The time–frequency analysis approach of electric noise based on the wavelet transform

In this paper, the wavelet transform approach has been firstly introduced to analyze electric noise in a transistor. Due to the multiresolution ability of wavelet transform, we can separate noise signal into several detail signals and approximation signal which can be interpreted in terms of the noise output of a generalized constant-Q filter bank and low pass filter, respectively.Based on this approach, the fractal and chaos characteristic of 1/f noise are obtained, the smaller burst noise pulse embedded in the white noise and 1/f noise can be detected, and the noise spectrum can also be calculated from short noise data. These results demonstrate that wavelet transform approach is a useful tool for investigation of noise mechanism of a transistor.     

Spatially adaptive wavelet-based multiscale image restoration

In this paper, we present a new spatially adaptive approach to the restoration of noisy blurred images, which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image. This is accomplished through a multiscale Kalman smoothing filter applied to a prefiltered observed image in the discrete, separable, 2-D wavelet domain. The prefiltering step involves constrained least-squares filtering based on optimal choices for the regularization parameter. This leads to a reduction in the support of the required state vectors of the multiscale restoration filter in the wavelet domain and improvement in the computational efficiency of the multiscale filter. The proposed method has the benefit that the majority of the regularization, or noise suppression, of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees. Not only does this lead to potential parallel implementation schemes, but it permits adaptivity to the local edge information in the image. In particular, this method changes filter parameters depending on scale, local signal-to-noise ratio (SNR), and orientation. Because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image, this algorithm may be viewed as an "edge-adaptive" multiscale restoration approach.