A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.

On the aliasing error in a class of bidimensional wavelet subspaces

This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an

Vector sampling theorem for wavelet subspaces

The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.

The Properties of Finitely Generated Shift-invariant Subspace in L_(2π)~2

In this paper, some properties of shift invariant subspace in Periodic wavelets theory are discussed.

Two-direction refinable functions and twodirection wavelets with high approximation order and regularity

The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.

Biorthogonal Wavelet Based Algebraic Multigrid Preconditioners for Large Sparse Linear Systems

In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.

An Improved Wavelet Based Preconditioner for Sparse Linear Problems

In this paper, we present the construction of purely algebraic Daubechies wavelet based preconditioners for Krylov subspace iterative methods to solve linear sparse system of equations. Effective preconditioners are designed with DWTPerMod algorithm by knowing size of the matrix and the order of Daubechies wavelet. A notable feature of this algorithm is that it enables wavelet level to be chosen automatically making it more robust than other wavelet based preconditioners and avoids user choosing a level of transform. We demonstrate the efficiency of these preconditioners by applying them to several matrices from Tim Davis collection of sparse matrices for restarted GMRES.

Construction tight wavelet of two-direction frames

We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results.

A Hybrid Coordinated Design Method for Power System Stabilizer and FACTS Device Based on Synchrosqueezed Wavelet Transform and Stochastic Subspace Identification

The occurrence of low-frequency electromechanical oscillations is a major problem in the effective operation of power systems. The scrutiny of these oscillations provides substantial information about power system stability and security. In this paper, a new method is introduced based on a combination of synchrosqueezed wavelet transform and the stochastic subspace identification (SSI) algorithm to investigate the low-frequency electromechanical oscillations of large-scale power systems. Then, the estimated modes of the power system are used for the design of the power system stabilizer and the flexible alternating current transmission system (FACTS) device. In this optimization problem, the control parameters are set using a hybrid approach composed of the Prony and residual methods and the modified fruit fly optimization algorithm. The proposed mode estimation method and the controller design are simulated in MATLAB using two test case systems, namely IEEE 2-area 4-generator and New England-New York 68-bus 16-generator systems. The simulation results demonstrate the high performance of the proposed method in estimation of local and inter-area modes, and indicate the improvements in oscillation damping and power system stability.

基于小波域平稳子空间分析的风力发电机齿轮箱故障诊断

风力发电机齿轮箱故障信号为非平稳瞬态微弱信号,容易被齿轮啮合信号及其他噪声淹没。提出一种融合连续小波变换(Continuous wavdot transform,CWT)和平稳子空间分析(Startionary subspace analysis,SSA)的信号分解方法并应用于风力发电机齿轮箱故障诊断中。平稳子空间分析作为一种盲源分离技术可将高维数据分解成平稳源部分和非平稳源部分,对待分析信号各分量间的独立性没有要求且不需要任何先验信息。连续小波变换则可利用其所具有的多尺度分析特性把一维时间序列转换为不同尺度下的多维时间序列。对观测得到的一维时间序列数据进行连续小波变换得到多维时间序列作为平稳子空间分析的输入,利用平稳子空间分析方法将该多维时间序列分解为平稳源信号分量和非平稳源信号分量,对非平稳源信号进行包络谱分析得到齿轮箱故障的特征频率。该小波域平稳子空间分析方法被应用于一个实际风力发电机齿轮箱振动信号的分析,试验结果表明该方法可有效地诊断出齿轮箱中的轴承故障。

地震子波提取方法综述

地震子波提取方法总体上可分为确定性子波提取方法、统计性子波提取方法两大类。确定性子波提取方法不需要对反射系数序列的分布作任何假设,能得到较为准确的子波,但很容易受各种测井误差的影响,尤其是声波测井资料不准而引起的速度误差会导致子波振幅畸变和相位谱扭曲;统计性子波提取不需要测井信息,也可以得到子波的估计,但需要对地震资料和地下反射系数序列的分布进行某种假设,所得到子波精度与假设条件的满足程度有关。文中对确定性子波提取方法和统计性子波提取方法进行了详尽的评述,并认为可将通信工程中的子空间分解法的思想用于混合相位子波提取。子空间法混合相位子波提取基于信号和噪声子空间正交的原理,建立二次型的目标函数,不需要对地层反射系数做任何假设,因此子波提取准确度高且稳定性好。

基于小波变换和NMF的人脸识别方法的研究

为了克服PCA、ICA等传统方法在人脸图像特征抽取时存在速度慢、识别率低的缺点,该文提出了一种将非负矩分解思想应用于人脸特征提取的算法。利用小波变换对人脸图像进行分解,对其中包含主要信息的低频子带运用NMF构造特征子空间,在子空间内实现识别。实验结果表明,该方法实用、有效,减少了计算量,提高了系统的识别率,使识别率达到90%以上,有着广泛的研究价值和应用前景。

Symlets小波和子空间联合增强下的语音识别

针对小波阈值选择的多样性,主要研究了小波自适应阈值消噪联合子空间增强对特定人汉语孤立词识别系统的鲁棒性提升。采用Mel倒谱系数,在基于矢量量化(VQ)和高斯混合模型(GMM)的两个系统上,检验采用联合Symlets小波多阈值消噪和子空间增强算法在互为先后顺序作用下系统的识别率,给出一个先Symlets小波阈值消噪再子空间增强的语音增强方法。人耳感官和Matlab实验证实该方法结合了两者的优点,不但平衡了语音失真和噪声抑制,亦可提高VQ系统的顽健性,而对于GMM系统作用有限。

子空间法单输入多输出系统混合相位地震子波提取

针对高阶统计量混合相位地震子波提取方法要求地层反射系数是非高斯白噪声,并且子波提取速度较慢的缺陷,提出子空间法单输入多输出系统(SIMO)混合相位地震子波提取方法,即基于信号和噪声子空间正交的原理,建立二次型的目标函数,通过对目标函数进行优化就可以提取出混合相位的地震子波,它不需要对地层反射系数做任何假设,因此完全不同于高阶统计量地震子波提取。模型试验和实际应用结果表明,子空间法SIMO系统混合相位子波提取速度快且准确度高,非常适合于无井和井资料不可靠地区的地震子波提取,具有广阔的应用前景。

基于运行检测的小波模态参数识别

众所周知结构的运行条件和实验室测试条件明显不同,在实验室中结构的特性可以较为准确的模拟,结构激励是已知的。但是对于正常使用的结构来讲,激励往往是不可测量的,同时大部分情况下是非稳态的。因此基于运行模态的结构分析方法被提了出来,并将它作为传统模态分析的一个补充方法。提出基于运行检测的小波模态参数识别技术,基于小波的模态参数识别是将信号变换到时(频域),这有利于识别结构的动态特征参数频率、阻尼和振型。给出运行情况下结构振动响应数据的小波变换的振幅和相位与特征频率及阻尼之间的关系。提出小波谱分析方法,并用它来识别结构的振型。数值模拟的例子表明,采用小波的识别方法所识别的结果与频域的峰值法和时域的随机子空间方法所识别的相符。

有限区间小波子空间上的采样定理及H^2(I)空间中函数的逼近表示

给出有限区间 [0 ,L ]小波子空间上的 Shannon型采样定理 .它是应用再生核空间理论和Riesz基的对偶性质得到的 .另外 ,根据得到的采样定理 ,讨论了 Sobolev空间 H20 ( I)和 H2 ( I)中的函数、一阶导函数及二阶导函数的逼近表示 .

用小波包改进子空间的语音增强方法

针对传统子空间语音增强方法中,由于不能去除整个噪声子空间而导致语音特征值估计的偏差,致使增强语音中仍有残留噪声的问题,提出一种新的用小波包改进的方法,该方法利用小波包对噪声的抑制功能,首先对带噪语音进行KL(Karhunen-Loeve Transform)变换,得到带噪语音的特征值,并对该特征值进行Daubechies8小波尺度分解,利用新的改进的软判决阈值函数去除一部分噪声子空间;然后再在子空间内用统计信息的方法实时跟踪此时噪声特征值,进一步消除所有噪声子空间,从而得到最终估计的语音特征值;最后由KL逆变换还原出纯净语音。仿真结果表明,在输入信噪比相同的情况下,经过该方法的增强语音的输出信噪比明显高于传统子空间方法,听觉感受上增强语音也具有更好的清晰度和可懂度。

基于子空间约束Huber范数的深度域地震子波提取

在常速度深度域,只有数百米深度范围的可用测井信息,相当于常速度深度域子波长度的2~5倍。因此,在常速度深度域中从"短数据"中提取可靠的地震子波难度较大。为此,提出了一种基于子空间约束Huber范数的深度域地震子波提取方法。实现过程为:将深度域反射系数、深度域井旁道通过速度变换转换到常速度深度域;给定初始子波和阈值,合成常速度深度域地震记录;计算合成地震记录与井旁地震记录的残差,并根据残差使用迭代最小二乘法更新地震子波,直至达到迭代终止条件。正演模型测试和实际数据应用结果表明,相较于一些常规方法,所提方法从较短的深度域数据中提取的地震子波更可靠,对于反映深度域地震子波随深度变化的特征,并根据需要提取深变地震子波具有重要意义。

低频振荡模态参数辨识的共振稀疏分解SSI分析方法

提出在色噪声背景下,采用共振稀疏分解的随机子空间法进行低频振荡模态参数的辨识,根据信号预知的共振属性实现复杂信号的分离。首先,对含高斯色噪声的低频振荡信号进行分解,得到高共振分量、低共振分量和余项三部分。低频振荡信号具有高共振属性,高共振分量即为提取的持续振荡的低频振荡信号,而高斯色噪声大部分存在于余项中。然后对高共振分量利用SSI进行参数辨识,得到较高参数的辨识准确度。仿真算例和实例说明了所提方法的有效性。

图像边缘检测的小波包分解算法

提出用于图像边缘检测的小波包分解算法.首先对图像的高频子空间进行多层次小波包分解,接着求出各层同一子空间不同方向上系数的差值,然后分层对差值进行阈值化处理,最后依据每层阈值化后的系数,得到不同分辨率下图像的边缘.该算法不需预先对图像进行去噪处理,却能很好地抑制噪声.实验结果表明,该算法既能根据需要分别求出不同尺度下图像的边缘,又能保持图像边缘的完整性和清晰性.