The continuous wavelet derived by smoothing function and its application in cosmology

The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet functions are obtained by taking the first derivative of smoothing functions with respect to the scale parameter. Due to this wavelet constructing scheme, the inverse transforms are only one-dimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms(CWTs) constructed in this way are more ready to use than the usual scheme. We then apply the Gaussian-derived wavelet constructed by our scheme to computations of the density power spectrum for dark matter, the velocity power spectrum and the kinetic energy spectrum for baryonic fluid. These computations exhibit the convenience and strength of the CWTs. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make CWTs very useful in practice.     

平板边界层转捩过程中低频信号的产生

利用Fourier频谱分析和小波变换处理在平板边界层转捩过程中测得的速度信号,观察到频谱中存在低于基本扰动波频率的含能信号,即文中所谓的低频信号.在进一步分析中,发现这种低频信号的产生可能与流动的间歇性有关.由于流动的间歇性导致速度信号的脉动,数据结构产生间歇变化,这种信号并不一定对应于流场中的某一物理结构的真实频率 关键词： 边界层 转捩 Fourier频谱分析 小波变换     

基于小波和神经网络的风机故障诊断系统设计

本文在LabVIEW平台下,设计了一种基于小波和神经网络的风机故障在线诊断系统。以风机产生的噪声为诊断依据,用噪声信号的功率谱重心、A声级、小波分解后相关频段的能量构成故障诊断的特征向量,以BP网络作为故障的智能分类器,建立起智能诊断系统。实验结果表明,采用小波和神经网络相融合的诊断与识别技术,是提取风机故障特征,进行状态识别的一种有效方法。所设计系统有较强的学习能力和容错能力。诊断结果比较可靠、准确。     

一种折中的小波阈值方法对γ能谱平滑处理的研究

采用小波软、硬阈值函数折中后的小波阈值方法对天然放射性环境下γ谱数据进行平滑处理。通过Matlab数据分析软件,分析对比了五种不同的平滑去噪方法:五点平滑法、傅里叶变换法、小波软阈值法、小波硬阈值法,以及折中的小波阈值方法。结果表明:折中的小波阈值方法在反映γ能谱特征的峰本比和峰总比分别为7.1609,0.3945,平滑去噪效果要明显优于其他四种方法,能最大程度地保留原始信号特征,具有较高的应用价值。     

一种改进的基于小波方向对比度的无缝拼接算法

为了提高图像无缝拼接效果,对现有平滑算法进行分析,在此基础上提出一种基于小波方向对比度的中缝平滑算法。该算法首先对源图像进行基于统计参数的预处理,使得图像整体亮度趋于一致,然后利用小波变换对图像进行多分辨率分解,对于分解后的图像提出采用一种基于改进的小波方向对比度的规则进行平滑处理。文中还通过几种图像客观评价标准对仿真结果进行了评价,结果表明：该方法在两图像灰度相差较大时也能够取得较好的平滑效果,对光照具有鲁棒性,并且平滑后的图像可以保留原始图像的细节信息,使得图像在保证清晰度的前提下达到无缝拼接。     

Multitarget Detection Using a Hybrid Optical Joint Transform Correlator with Power Spectrum Subtraction

Multitarget detection using a hybrid optical joint transform correlator with power spectrum subtraction is proposed. This architecture is a programmable single spatial light modulator joint transform correlator. It consists of a liquid crystal display panel, an imaging lens, and a liquid crystal light valve to enhance resolution and space-bandwidth production. In this technique, it has two joint images in the input plane. In the second joint image, the reference image is contrast-reversal. With this technique, the second joint power spectrum is subtracted from the first joint power spectrum and the subtracted joint power spectrum is then taken the inverse Fourier transform. This technique is found to yield better correlation output performance than that of the classical joint transform correlator. Computer simulation results and the optical experimental results for input scene of the multitarget are given.The results have verified the correctness of the system design and performance analysis.     

Multitarget Detection Using a Hybrid Optical Joint Transform Correlator with Power Spectrum Subtraction

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Method of improved scatterer size estimation and application to parametric imaging using ultrasound

The frequency dependence of RF signals backscattered from random media (tissues) has been used to describe the microstructure of the media. The frequency dependence of the backscattered RF signal is seen in the power spectrum. Estimates of scatterer properties (average scatterer size) from an interrogated medium are made by minimizing the average squared deviation (MASD) between the measured power spectrum and a theoretical power spectrum over an analysis bandwidth. Estimates of the scatterer properties become increasingly inaccurate as the average signal to noise ratio (SNR) over the analysis bandwidth becomes smaller. Some frequency components in the analysis bandwidth of the measured power spectrum will have smaller SNR than other frequency components. The accuracy of estimates can be improved by weighting the frequency components that have the smallest SNR less than the frequencies with the largest SNR in the MASD. A weighting function is devised that minimizes the noise effects on the estimates of the average scatterer sizes. Simulations and phantom experiments are conducted that show the weighting function gives improved estimates in an attenuating medium. The weighting function is applied to parametric images using scatterer size estimates of a rat that had developed a spontaneous mammary tumor.     

基于小波系数图和卷积神经网络的太赫兹光谱物质识别

许多太赫兹光谱物质识别方法依靠寻找该物质在太赫兹波段范围内不同光谱表现出的不同特征来识别特定物质。吸收峰提取法是常用的光谱特征提取算法,但当光谱无明显特征吸收峰或峰位、峰值相近或难以识别时,难以利用吸收峰特征辨别物质。将机器学习和统计学习技术用于太赫兹光谱的识别中虽减少了吸收峰的干扰,但常常需要人为定义特征而导致分类误差。深度学习法能自动提取特征,但在识别前往往需要进行复杂的预处理操作,并且在特征提取的过程中容易丢失部分特征从而导致分类误差。针对以上问题,提出了一种基于小波系数图和卷积神经网络的太赫兹光谱识别方法。利用太赫兹光谱信号进行小波变换时,由于小波系数矩阵的每一行系数与原始光谱信号存在着对应关系,因此将太赫兹光谱的吸收系数通过小波变换在频率域上展开,能得到不同的二维的频率-尺度分布图,又称小波系数图。然后构造一个卷积神经网络(CNN)对小波系数图进行分类,可得到太赫兹光谱物质的分类结果。为了验证所提出算法的有效性,将三组小波系数图数据与原始光谱数据分别输入CNN、Support Vector Machin (SVM)、Multilayer Perceptron (MLP)三种不同的分类器作对比,从实验结果可以发现本文算法在三组数据中的识别率均达到了100%,说明相比于传统方法,本文方法能准确分类没有明显特征吸收峰的光谱,证明了使用卷积神经网络识别小波系数图的有效性。为了体现本文算法的优势,与小波脊线寻峰识别算法作对比,实验结果表明本文算法几乎不受峰频、峰位、峰值的影响,无论是识别不存在吸收峰的淀粉,还是识别相似度高的蔗糖和葡萄糖,都具有较高的识别率,分类准确率达97.62%,证明了所提算法的优越性。该算法为太赫兹光谱数据识别提供了一种新思路,同时也可以推广运用到其他谱图物质的识别中。     

Extended fractional wavelet joint transform correlator

An extended fractional wavelet joint transform correlator is implemented for real-time target recognition applications. The real-time input scene captured using a charge-coupled device camera along with the reference image is fractional Fourier transformed. The obtained joint power spectrum is multiplied by an appropriately scaled wavelet filter and the resultant function is differentiated. The application of wavelet filter enhances the correlation outputs and differential processing of wavelet-filtered joint power spectrum improves the detection efficiency by reducing the zero-order spectra. Targets with Gaussian and speckle noise have also been used to check the correlation output. The performance metrics: correlation peak intensity, peak-to-correlation energy, peak-to-sidelobe ratio and signal to clutter ratio have been calculated. The experimental results are presented in support of the proposed idea.     

遥感相机自动检焦技术研究

将基于图像处理的自动检焦技术应用于线阵CCD推扫成像的空间遥感相机中。图像法检焦的关键在于对焦评价函数的选取。通常对焦评价函数是在摄影目标不变的情况下得出的,而推扫成像的线阵CCD相机在任意时刻所拍摄的景物都是不同的,这就给对焦评价函数的选取增加了难度。用功率谱的方法对任意景物在空间频域进行分析表明,功率谱对于自然景物具有一定的不变性。由此建立了基于功率谱的对焦评价函数,采用小波去噪与亮度归一化相结合的图像预处理技术有效地去除了图像噪声和亮度变化对对焦精度的影响。通过对功率谱评价函数进行加权处理,提高了对焦评价函数曲线的灵敏度。仿真实验表明了所构造的对焦评价函数是可行的。     

一种基于小波变换的红外偏振融合算法

针对红外偏振图像可以较好地抑制背景噪声,对目标边缘信息比较敏感的特点,提出一种基于小波变换的红外偏振融合算法,它主要用于红外辐射强度图像和偏振度图像融合,增加图像的信息量。首先采用小波变换对参与融合的每幅图像分别进行各尺度分解,得到各尺度小波系数,然后针对不同尺度小波系数,采用邻域平均梯度为判据进行融合,得到融合后的各尺度小波系数,最后通过小波逆变换进行图像重构,得到融合图像。融合前后的图像对比表明融合图像在保留辐射强度图像的清晰度的同时,突出了目标的边缘、轮廓信息。相对于辐射强度图像,融合图像的梯度均值提高了112%,相对于偏振度图像,融合图像的标准差提高了151%,信息熵提高了38%。     

Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter

A spatially adaptive two-dimensional wavelet filter is used to reduce speckle noise in time-domain and Fourier-domain optical coherence tomography (OCT) images. Edges can be separated from discontinuities that are due to noise, and noise power can be attenuated in the wavelet domain without significantly compromising image sharpness. A single parameter controls the degree of noise reduction. When this filter is applied to ophthalmic OCT images, signal-to-noise ratio improvements of >7 dB are attained, with a sharpness reduction of <3%.     

光谱去相关技术在高光谱图像小波压缩中的应用

随着数据量的不断增长,如何有效压缩高光谱图像成为影响其普及应用的一个关键问题。近年来,小波压缩技术已经被证明是高光谱图像压缩方法中很有发展前景的一个,但由于其对高光谱图像特性的利用较为有限而使其性能的进一步提升受到了限制。文章根据高光谱图像的光谱特征,提出了一种基于光谱去相关的高光谱图像小波压缩方法,设计了分块预测方法来同时去除光谱间相关性和空间相关性,并将其应用于小波压缩方法之中。首先,将高光谱图像分为几个具有高谱间相关性的图像块。然后推导出各块中波段的近似成比例的特性,并在各块分别进行基于这一特性和超光谱图像其他特性设计波段预测编码。最后,将预测用的参考波段和预测后获得的偏差数据,通过小波编码技术进行压缩。实验结果表明,所设计的方法与目前先进的超光谱压缩技术相比其性能有显著的提升。与AT-3DSPIHT算法比较,最高PSNR或SNR提升幅度均能达到4.2 dB左右。此外,此方法在低比特率下的优势也十分突出。     

Simulation of Properties of Images with Atomic Resolution in a Scanning Probe Microscope

A method for simulation of images in a scanning probe microscope (SPM) using simultaneous wavelet transform and median filtering is proposed. The wavelet transform with the fourth-order Daubechies kernel is used. Such a transform makes it possible to select details of different scales in the SPM image and, hence, study fractal properties of surfaces. Simulation is used to show that ultrahigh (atomic) resolution is possible in SPM provided that the size of the contact region in the probe–sample system is significantly greater than atomic size and the lattice atoms are randomly distributed. Contrast inversion in the SPM images in the multiscan mode is interpreted.     

舰船噪声小波谱提取方法研究

人耳听测舰船噪声的特征,是声纳员非常重要的专业技能。本文根据小波变换与人耳蜗频率响应相近似的特点,以cmor1-0.5母小波为基础,构造了一系列基于小波变换的滤波器组。对于小波谱提取中涉及的带宽、分辨率等参数进行了分析,提出了小波谱提取过程中改善分辨率的办法。为检验该方法的可行性,对三种不同类型的舰船噪声进行了小波谱分析,与其FFT谱图进行了比较。为解决小波谱提取过程中高分辨率与计算量的矛盾,提出了对指定频带进行小波谱分析的方法,解决了计算量的问题。     

Modified wavelet based morphological correlation for rotation-invariant recognition

A wavelet-based rotation invariant morphological correlation (WBRIMC) is proposed as a new architecture to improve the properties of the classical rotation invariant morphological correlation (RIMC). For the WBRIMC, the JPS of the RIMC is filtered by an appropriately dilated power spectrum function of wavelet. Simulation results confirm that the WBRIMC has higher discrimination capability with sharp and intense correlation signals, and is more tolerant to the salt-and-pepper noise and white additive Gaussian noise than is the Circular harmonic filter (CHF), the phase only CHF (POCHF) and the RIMC.     

Complex denoising of MR data via wavelet analysis: application for functional MRI

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.     

基于小波变换的解相技术研究

提出一种基于小波变换的频域解相技术。对调制栅线图像进行小波变换,生成被测物体背景图像,两幅图像相减得到相对变形栅线图像,分析基频谱,由于背景成分基本消除,利于有用频带的提取,可以实现大梯度变化曲面和复杂形面的自动轮廓测量。     

Long-range dependence in North Atlantic sea level

Sea level is an important parameter in climate and oceanographic applications. In this work the scaling behavior of sea level is analyzed from time series of sea level observations. The wavelet domain is particularly attractive for the identification of scaling behavior in an observed time series. The wavelet spectrum from a scale-by-scale wavelet analysis of variance reproduces in the wavelet domain the power laws underlying a scaling process, allowing the estimation of the scaling exponent from the slope of the wavelet spectrum. Here the scaling exponent is estimated in the wavelet domain for time series of sea level observations in the North Atlantic: at coastal sites from tide gauges, covering 50 years of monthly measurements, and in the open ocean from satellite altimetry, covering 12 years of satellite measurements at 10 days intervals. Both tide gauge and altimetry time series exhibit scaling behavior. Furthermore, the degree of stochastic persistence is spatially coherent and distinct at the coast and in the open ocean. Near the coast, the stochastic structure of the sea level observations is characterized by long-range dependence with a moderate degree of persistence. Larger values of the scaling exponent, consistent with weaker persistence, are concentrated in the northern Atlantic. At mid-latitudes the stochastic dependence of sea level observations is characterized by strong persistence in the form of strong long-range and 1/f dependence.