An imaging device that uses the wavelet transformation as the image reconstruction algorithm

Many imaging devices have been constructed that use fourier transform techniques for image reconstruction as well as for image analysis. The basis functions in the fourier transform space are sinusoids. These are not localized. Therefore it should not be expected that highly localized behavior of a signal be characterized well using functions distributed evenly throughout the interval of the integral transform. Also, the phase cancellations of a conventional impulse signal are not handled well by fourier techniques. On the other hand, the basis functions of the wavelet transformation are highly localized, i.e., these exhibit compact support, yet are orthonormal. The multispectral decomposition algorithm of the wavelet transformation is used to analyze the signal returning from the reflections of a single ultrasonic transducer with a focused beam and operated in the focal zone. The choice of frequency depends upon the mutually antagonistic factors of penetration (αf^–2) and resolution (αf). The signal sent into the sample should not be the impulse response signal used in conventional devices; rather, it should be a time-reversed replica of a single or a linear combination of the most highly localized basis function wavelets. The returning signal is a sequence of translates of the wavelets plus perhaps some lower-resolution wavelets. The translations are proportational to the time of flight of the signal. The wavelet transformation is superb at discriminating the population of each of these translates which is identically the A-scan signal. The transmitted signal, which is a time-reversed single wavelet or a linear combination of wavelets, is not easy to produce. Inexpensive ultrasound transducers have resonances which make it difficult to produce any desired wave form. Wavelet shape is far from arbitrary. Precise wave shaping is performed by measuring the impulse response function of the transducer; then, the desired wave shape is convolved with the inverse of the measured impulse response function of the transducer. This produces the signal to be presented to the pulse generation circuit. Care is taken to damp the impulse response so that there are no zeros. The received signal is sampled at an even rate which is carefully chosen to match the time delay of one wavelet translate to the next. B-scan, C-scan, and volume imaging are easily accomplished using a sequence of A-scan data, all by conventional techniques. A single A-scan requires less than 2 ms to perform and reconstruct with a high-speed arithmetic unit which was designed in conjunction with this work and is now commercially available.     

双树复小波域隐Markov树模型降噪及在机械故障诊断中的应用

提出一种基于双树复小波变换的隐Markov树模型的信号降噪方法,并将其成功应用于机械故障诊断中。机械设备的振动信号中不可避免的存在着噪声,使得微弱故障信息的提取一直是故障诊断的难点和热点。双树复小波变换具有近似平移不变性,而隐Markov树模型能有效刻画小波系数间的相关性和非高斯性,两种优势的结合可以获得比常规软、硬阈值小波降噪法和小波域隐Markov树模型降噪法更好的降噪效果。它不仅能有效抑制高斯白噪声,还能够去除异常冲击干扰,仿真信号验证了这一点。对于实际滚动轴承信号,使用该方法同样可以获得满意的结果     

Reducing the condition number for microlocal discretization problems

In this paper, we analyse the conditioning properties of systems arising from microlocal discretizations. These systems use oscillating basis functions to model wave problems in harmonic regime. Facing severe condition numbers, we first interpret the difficulty as coming from an over-discretization, which creates evanescent waves. The first solution we investigate is to project the problem onto the orthogonal of these modes. This is done on a model problem but it is not a satisfactory solution on real-sized systems. Then we propose to transform the linear system by using a wavelet basis. It appears that this transformation discriminates strongly between small and big matrix coefficients. This allows us to threshold the transformed system to obtain a reduced one which is both better conditioned and smaller. The use of wavelets is original, since the transformation is done in the spectral domain thanks to the microlocal discretization. We finally obtain a method that uses between one and two degrees of freedom by wavelength to simulate scattering problems.     

高速高精度的机器视觉定位的算法

针对IC装备的视觉系统在复杂条件下很难快速、精确定位这一问题,提出了基于小波变换和径向基函数（RBF）网络算法,此算法提取图像归一化小波系数作为特征矢量,对目标图像特征进行学习,得到RBF分类器,利用它在背景图像上进行目标定位。仿真实验表明,此算法可以实现在旋转、平移、尺度变化和噪声条件下的快速定位,定位精度达到亚像素级。     

复合评定法在三维粗糙表面评定中的应用

提出一种将双树复小波与分形理论相结合的复合评定方法。即利用双树复小波近似的平移不变性和方 向性好等优点,将信号分解成更为细腻的低频和高频信号,同时根据多尺度下信号分形维数的不变性,利用图像灰 度值自相关求得高低频信号的分形维数,通过计算高低频信号分形维数之间的差值（即分形维数距)来确定双树复 小波的分解尺度。仿真结果表明复合评定法可以较好地提取基准面,且分形维数距确定分解层数的准确性通过均 方根*Sq值得到了验证;两个实例均说明,复合评定法可以很好地提取具有分形特征的纳米级三维粗糙表面基准或 波纹度,为实际工程表面评定提供了可靠的理论基础。     

自适应冗余提升小波降噪分析及其在轴承故障识别中的应用

为有效识别机械设备中滚动轴承的微弱故障信息,本文提出一种自适应冗余提升小波降噪方法。根据待分解低频尺度系数所含的不同特征,应用范数准则来自适应地选取最匹配于该尺度系数特征的小波函数。同时,引入多孔算法,用以通过冗余性来保证逐层分解后各尺度系数和小波系数所含有的丰富的信息量。接下来,对各层小波系数采用变尺度阈值降噪算法,并对降噪后的系数进行重构及包络谱分析,进而提取滚动轴承的故障特征。应用上述方法分别对轴承实验台轴承混合故障信号和现场实际信号进行分析,均较好地实现了故障识别,验证了本文方法的有效性。     

Wavelet variance, Allan variance, and leakage

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the variance of a time series on a scale by scale basis. The wavelet variance corresponding to some of the recently discovered wavelets can provide a more accurate conversion between the time and frequency domains than can be accomplished using the Allan variance. This increase in accuracy is due to the fact that these wavelet variances give better protection against leakage than does the Allan variance     

离散余弦小波包变换及语音信号压缩感知

针对语音信号压缩感知问题,在研究语音离散余弦变换(Discrete Cosine Transform,DCT)系数和小波包变换(Wavelet Packet Transform,WPT)特性的基础上构造了离散余弦小波包变换(Discrete Cosine Wavelet Packet Transform,DCWPT)。DCWPT首先获取语音信号的DCT域系数,结合语音频谱特性选取部分DCT系数进行WPT变换,从而得到比DCT系数更加稀疏的DCWPT系数。为将此变换直接用于压缩感知,构造了DCWPT的正交稀疏分解矩阵并分析了其稀疏表示性能。结合稀疏表示基优化了正交匹配追踪重构算法,提出了基于DCWPT的语音信号压缩感知框架。通过压缩重构对照实验,采用主客观评价指标,得出该方法优于传统基于DCT的语音压缩感知方法的结论。     

A hybrid contextual compression technique using wavelet and contourlet transforms with PSO optimized prediction

Contextual compression is an essential part of any medical image compression since it facilitates no loss of diagnostic information. Although there are many techniques available for contextual image compression still there is a need for developing an efficient and optimized technique which would produce good quality images at lower bit rates. This article presents an efficient contextual compression algorithm using wavelet and contourlet transforms to capture the fine details of the image, along with directional information to produce good quality at high Compression Ratio (CR). The 2D discrete wavelet transform, which uses the simplest Daubechies wavelets, db1, or haar wavelet, is chosen and used to get the subband coefficients. The approximate coefficients of the higher subbands undergo contourlet transform employing length N ladder filters for capturing the directional information of the subbands at different scale and orientations. An optimized approach is used for predicting the quantized and the normalized subband coefficients resulting in improved compression performance. The proposed contextual compression approach was evaluated for its performance in terms of CR, Peak Signal to Noise Ratio, Feature SIMilarity index, Structure SIMilarity Index, and Universal quality (Q) after reconstruction. The results clarify the efficiency of the proposed method over other compression techniques.     

阈值改进整数小波与LZW算法相结合的水声数据压缩方法

提出一种阈值改进整数小波与基于字典编码的LZW(Lempel-Ziv-Welch)算法相结合的数据压缩方法,该方法旨在减少水声数据传输量的同时尽可能地达到高保真。数据压缩过程中,先对水声数据进行整数小波变换,再对变换后的高频系数采用改进的小波阈值算法和阈值函数进行处理,提高了数据压缩倍数和信噪比,降低了误差。最后通过LZW将处理后的系数进行编码输出,进一步提升压缩效果。文中给出了相应的数据压缩算法流程。实际舰船辐射噪声数据的压缩处理结果表明,该方法能有效提高信号信噪比、减少信号失真并能获得更大的压缩倍数。     

The construction of 1D wavelet finite elements for structural analysis

Adopting the scaling functions of B-spline wavelet on the interval (BSWI) as trial functions, a new finite element method (FEM) of BSWI is presented. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The transformation matrix is the key to construct wavelet-based elements freely as long as we can ensure its non-singularity. Then, classes of C₀ and C₁ type elements are constructed. And the lifting scheme of BSWI elements is also discussed. The numerical examples indicate that the BSWI elements have higher efficiency and precision than traditional finite element method in solving 1D structural problems especially for geometric nonlinear, variable cross-section and loading cases.     

Tissue characterization using the continuous wavelet transform. Part I: Decomposition method

In this paper, a novel decomposition of the RF ultrasound signal into its coherent and diffused components is proposed. This decomposition is based on thresholding the energy of the continuous wavelet transform of the RF signal using appropriate wavelets. The two components are modeled separately, and the model parameters are estimated. Previous work (Cohen et al. 1997) required assumptions about the periodicity of the coherent scatterers in the tissue. These assumptions are not necessary in this work. The decomposition algorithm is tested on simulated RF images. The accuracy of the estimated parameters is presented as well as the performance of the algorithm in low coherent-to-diffuse components' energy ratios (SNR)     

基于边缘检测的邻域加窗图像去噪算法

针对目前图像去噪算法中,消除噪声的同时又破坏边缘细节信息的问题,本文提出了结合边缘检测及邻域加窗的新算法.该算法采取平稳小波基以保持相位不变性,对低频和高频子带进行边缘检测,并将检测后的边缘信息选择后融合,即可得到原图像近似的边缘信息.依据小波方向性特点和层内相关性原理,对不同的子带在非边缘信息处采用不同的模板进行加窗处理.实验结果表明,该方法在降低了图像噪声的同时又尽可能地保留了图像的细节,较好地复原了图像.     

一种紧支集双正交小波基的构造

基于对偶尺度函数及对偶小波，提出了一种构造紧支集双正交小波基的算法，并给出严密的证明和推导过程。应用该算法，结合函数优化方法，构造出一系列包括样条小波、接近正交的双正交小波及其它具有特殊性质的双正交小波。该构造算法丰富了小波理论，可以广泛应用于信号分析、图像处理等领域。     

Motion estimation and compensation based on almost shift-invariant wavelet transform for image sequence coding

There has been rapid progress in the application of wavelet transforms to image and image sequence compression. The standard discrete wavelet transform lacks transition invariance in image decomposition which will affect the accuracy of motion estimation from the decomposed subimages in video coding. In this article, we present a study of applying an almost shift-invariant wavelet transform with “oversampled frames” to image sequence compression. With minimal oversampling and biorthogonal spline wavelets in the almost shift-invariant wavelet transform, motion vectors can be more accurately estimated, contributing toward fewer prediction errors in comparison to those obtained with the standard discrete wavelet transform. Thus, an improved compression ratio can be obtained. We present two new algorithms, the full-motion oversampling algorithm (FMOS) and the reduced search multiresolution motion estimation algorithm (MRME), for estimating motion fields at different scales and in different subimages. In the latter, motion vectors at a higher resolution are approximated by the motion vector estimates at a lower resolution through proper scaling. Experiments were performed on three video sequences with a variety of motions including slow, fast, and zooming. Our results have shown that both algorithms, FMOS and MRME, using the almost shift-invariant oversampled frame wavelet transform have reduced prediction errors and enhanced the compression performance in terms of peak-signal-to-noise ratio (PSNR) for the same bit rate when compared to the existing full motion standard algorithm. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 214–229, 1998     

邻域比较数字滤波与小波变换在脑电信号消噪中的应用

提出了邻域比较与小波变换相结合的脑电信号消噪方法,并利用这种方法对含有脉冲噪声的脑电信号进行消噪。首先介绍了邻域比较滤波的算法和小波变换消噪的原理,然后对实测的10例脑电信号进行消噪处理,最后将两种方法相结合的消噪效果与小波变换的消噪效果进行对比。实验结果表明,无论是信噪比还是均方根误差,两种方法相结合的消噪效果均优于小波变换的消噪效果。     

改进提升小波变换的空间频率比图像融合

提出了一种新型图像融合算法.该算法在提升小波变换的基础上,通过取消其奇偶分裂环节,得到具有平移不变性的非采样提升小波变换.对图像经非采样提升小波变换后的低频分量首先定义一种空间频率比,再通过空间频率比来计算融合因子,然后采用加权与选择相结合的方法对低频分量进行融合.高频分量直接选择一种基于边缘信息的加权融合方法.最后通过非采样提升小波逆变换重构得到融合图像.实验结果显示,该算法相对传统的图像融合算法能更好地描述灰度的突变信息,获得含有丰富细节特征的融合图像.     

Noise reduction for doppler ultrasound signal based on the adapted local cosine transform and the garrote thresholding method

In this paper, a novel approach, using the adapted local cosine transform combined with the non-negative garrote thresholding, is proposed to remove noise from the Doppler ultrasound signal. In the proposed approach, the local cosine transform is first performed on the signal of interest followed by a search algorithm to select the best basis. Then the coefficients of the obtained best basis are thresholded based on the non-negative garrote thresholding method. By means of the thresholded coefficients of the best basis, the signal is reconstructed. In the simulation study, the estimation precisions of the mean frequency waveform and the spectral width waveform are studied for the signal after denoising. The simulation and clinical results have shown that the proposed approach is superior to ones based on the wavelet transform, especially under low signal-to-noise ratio (SNR) circumstances.     

基于二进小波的雷达干涉图条纹探测相位解绕

以二进小波和相位解绕理论为基础，利用二进小波变换的快速算法，对雷达干涉条纹图进行多尺度相位突变边缘探测，进而根据信号和噪声的奇异性在二进小波变换下的局部模极大值随尺度变化的不同演化规律，提出了对雷达干涉条纹图的噪声有一定压制的基于二进小波的干涉条纹检测的相位解绕算法，结果表明，在噪声没有严重破坏相位突变边缘的情况下，相位解绕结果是令人满意的。     

自适应神经网络模糊小波语音消噪算法

针对有色噪声,采用自适应神经网络模糊系统模糊(Auto Neural Fuzzy Inference System,ANFIS)逼近有色噪声,利用自适应神经模糊推理系统ANFIS对噪声的非线性动态特性进行建模,提出了语音自适应神经网络模糊小波消噪算法,建立并训练了消噪系统。对被有色噪声污染的测量信号经模糊消噪后,根据信号和噪声的小波系数在不同分解尺度上的传递性,进行中值滤波和小波重构,得到了干净的语音。对算法进行了仿真实验,结果表明,消噪效果明显。