Estimation of optimal parameters of the multiplicative algorithm of wavelet filtering of images

In most widely used wavelet filtering algorithms, the decomposition coefficients are processed with the use of threshold functions, which makes it possible to account for the “energy” feature of each decomposition coefficient. To some extent, this disadvantage is removed in a class of multiplicative algorithms, which account for the energy of decomposition coefficients located in a given proximity from a processed decomposition coefficient. However, the effective error minimization in wavelet filtering of images requires that a parameter, the choice of the optimal value of which remains to be an unsolved problem, is introduced into these processing algorithms. Therefore, the problem solved in this paper is the estimation of the optimal value of this parameter, which minimizes the root-mean-square error of the filtering. The performed studies showed the effectiveness of the proposed estimation algorithm and the possibility of its use in practice.     

A new iterative algorithm for kinematic synthesis of gear drives for optimal speed ratio

The double composite gear trains offer attractive design features. However, their analysis using the algebraic equations method involves lengthy and tedious manual manipulations. The existing theories of composite gear trains is useful in this process to some extent, but it will not facilitate development of an algorithm suitable for all kinematic versions of a drive. The present algorithm based on the Unified Theory has been used for analysis of all the 18 versions of the drive with similar structure. The input data is simplified to that of feeding values of index exponents for the applicable versions. The optimal version of the twelve speed drive is synthesized with the present algorithm from the 18 versions belonging to open type having similar structure.     

一种综合小波变换的心电信号消噪算法

针对心电信号中混有的基线漂移、工频干扰、肌电干扰等噪声,比较了适于心电信号的4种基于小波变换的心电信号消噪算法,结合消噪后的信噪比和信号失真度,提出一种综合小波变换的心电信号消噪算法.该算法先使用小波分解法消除心电信号中的基线漂移,再利用模极大值法消除工频干扰、肌电干扰等噪声.并且运用该算法对MIT-BIH心律失常数据库中的含有多种噪声的心电数据进行了仿真与实验,结果表明噪声被有效地消除并且失真度较小,可满足临床分析与诊断对心电波形的要求.     

Quasi-optimal algorithm of estimating the coefficients of wavelet expansions during signal filtration

The proposed algorithm calculates its own filtration factor for each coefficient of the wavelet expansion of a noisy signal. The optimal filtration factor depends on the signal-to-noise ratio, which is estimated with a specially constructed iterative procedure. The limit points of this procedure are determined. A computational experiment performed shows that the proposed approach can be effectively used in problems of filtration and compression of noisy signals and images.     

Estimation of optimal threshold values in algorithms of wavelet filtration of images

A new algorithm is proposed for estimating optimal threshold values in thresholding algorithms of wavelet filtration of signals and images. Numerous computational experiments are performed to compare this threshold with threshold values widely used in wavelet filtration algorithms. Application of the proposed threshold is demonstrated to ensure substantial reduction of the filtration error of both smooth and high-contrast images.     

Maximum kurtosis principle for the parameter selection of Gabor wavelet and its application to ultrasonic signal processing

The noise suppression techniques with wavelet transform (WT) are widely used in nondestructive testing and evaluation (NDT&E), especially in ultrasonics. But the wavelet based filter has the property of equal Q-factor, so, it is impossible to choose the central frequency and the bandwidth arbitrarily at the same time. This paper develops a new technique using WT to eliminate this drawback. In this paper, a weak ultrasonic signals identification method by using the optimal parameter Gabor wavelet transform is proposed. We address the choice of the optimal central frequency and bandwidth of the Gabor wavelet using the kurtosis maximization algorithm. The central frequency and bandwidth of the optimal parameter Gabor wavelet matched that of the ultrasonic signal very well. Numerical and experimental results have been presented to evaluate the effectiveness of the optimal parameter Gabor wavelet transform on ultrasonic flaw detection. This technique is a simpler and effective technique for processing heavy noised ultrasonic signals.     

基于小波变换及FFT算法的涡街信号处理

近年来涡街流量计的应用越来越广泛,但在实际使用时管道振动和流场扰动等引起的噪声易对涡街信号造成干扰,导致实际测量精度达不到要求。本文使用小波变换及FFT算法对涡街信号进行处理。该方法对涡街信号提取和去除噪声效果良好。有利于扩大涡街流量计的量程范围,提高测量精度。     

基于稀疏小波变换的超宽带低信噪比信号检测算法

脉冲超宽带信号是时域瞬态脉冲,功率谱密度极低,在远距离通信时,信号淹没在噪声中较难检测,对前端采样率要求较高.针对脉冲超宽带低信噪比检测问题,提出了一种在脉冲波形先验信息已知条件下,基于稀疏小波变换的低信噪比检测方法.针对超宽带信号在小波域具有稀疏分布这一特征,依据压缩传感理论,分析并仿真了稀疏基矩阵选择时域采样矩阵和小波矩阵时,信噪比对于性能的影响,提供了重构算法中迭代终止门限的选择方法.仿真实验表明,相对于稀疏基矩阵为时域采样矩阵,采用小波变换矩阵可以在较低信噪比条件下实现超宽带信号的降噪重构.     

ECT图像重建正则化参数选取新方法

电容层析成像图像重建是一不适定反问题。此种情况下，仅使用最小二乘法不能保证获得满意的介质分布图像重建结果，因此广泛使用TIkhonov正则化算法来产生适当的解。正则化参数的合适选取对图像重建至关重要，其对重建质量和计算时间都有影响。本文提出了一种基于最平坦斜率的Tikhonov正则化参数选择方法，并针对2种典型介质分布，将基于此方法计算的正则化参数同L-曲线法在电容测量数据无噪声和施加噪声情况下的图像重建结果进行了比较。     

基于改进阈值小波算法的汽车轮速信号处理

在汽车制动过程中,轮速信号中的噪声对制动有着直接的影响,运用小波理论可以对轮速信号中的噪声进行去噪处理。噪声的幅值随着小波变换尺度的增加会逐渐减小,而信号的幅值与小波变换的尺度变化无关。在Donoho的软、硬阈值去噪方法基础上,提出了一种新的阈值函数量化法,该方法克服了硬阈值法不连续性和软阈值法有偏差的缺点,并把它们应用在汽车轮速信号的去噪上。新的阈值函数具有物理意义清晰、表达式简单等优点。实际信号处理结果表明,这种经改进的方法可以有效地去除噪声干扰,在信噪比指标上也明显优于常用的软、硬阈值去噪算法。     

基于谐波小波和Prony算法的转子不平衡信号提取

高精度动平衡测量系统中的信噪比很低,尤其是在邻近频率干扰背景下,常规的快速博里叶变换(fast Fourier trasformation,FFT)等方法无法准确提取不平衡信号.提出一种基于谐波小波和Prony算法的不平衡信号提取方法,先采用自适应谐波小波带通滤波提高信噪比,然后以滤波后的数据作为样本,采用Prony算法识别不平衡信号的幅值和相位,有效解决了邻近频率干扰导致的不平衡信号无法准确提取的问题.仿真和实验结果表明,该方法具有精度高、重复性好等优点,特别适合于信噪比较低的高精度动平衡测量系统中.     

Digital lock-in algorithm and parameter settings in multi-channel sensor signal detection

In order to implement demodulation of multi-channel composite signal in sensor signal detection system with high accuracy and high speed, in this paper we present a demodulation algorithm and schemes on how to optimize performances in detail based on the idea of software radio. A multi-channel composite signal was demodulated by the algorithm combined with a high-speed digital lock-in algorithm based on oversampling. To further enhance the signal-to-noise ratio, we discussed how to cut down crosstalk between adjacent channels, and a cascade filter was proposed. The result is helpful to effectively set carrier frequencies, from which a method of choosing parameters in frequency division multiplexing is obtained. Theoretical analysis shows that the new method has advantages such as high accuracy, high speed, and wide application range. It is suitable for sensor signal detection with AC signal excitation, and it can also improve overall system performance.     

基于灰色预测恢复算法的流式细胞仪多参数提取

针对流式细胞仪测控系统由于脉冲信号信息不完整导致多参数提取存在误差的问题,提出了一种基于灰色预测恢复算法的多参数提取方法。利用基于GM(1,1)模型的灰色预测梯形递推信号恢复算法对脉冲信号进行高精度恢复,提高信号的信息完整性。同时,对直流恢复模块进行了优化设计,通过高速数字信号处理芯片对脉冲信号模拟偏移量及直流恢复进行反馈,提高直流恢复精度及信号信噪比。最后,搭建了测控系统实验环境,对该系统进行了验证。实验结果表明,多参数提取精度均在±1.5%范围内;同时可以将流式细胞仪检测细胞的速度提高到10万个/s。     

电容层析成像图像重建的总变差正则化算法

针对电容层析成像（ECT）逆问题解的不适定性,本文提出一种基于总变差（total variation,TV）正则化的图像重建算法。同传统的2范数Tikhonov正则化方法相比,该算法（基于1范数正则化）不仅保证了逆问题求解的稳定性,而且提高了对介质非连续分布的区域成像的分辨能力,具有良好的保边缘性。仿真及实验结果表明,该算法在重建图像质量和重建速度两方面均具有优势。     

Localization algorithm for small objects in an image using wavelet transforms

This paper presents an algorithm for determining the coordinates of small objects appearing in a sequence of scene images based on sum and difference processing of the detailing wavelet coefficients of the current and reference images, followed by a morphological analysis of the generated pseudo-image. The effectiveness of the algorithm is compared with the difference algorithm for analyzing changes in the observation scene. It is shown that the proposed algorithm is more resistant to the effects of relative shifts of the current and reference images.     

An algorithm for the continuous Morlet wavelet transform

This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.The energy values of the wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given.The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.     

Numerical experiments on determination of spatially concentrated time-varying loads on a beam: an iterative regularization method

This paper treats a solution for the ill-posed (inverse) load determination problem for a time-varying load on a beam. The ill-posed nature of the problem causes numerical instability. Conventional numerical approach for solutions results in arbitrarily large errors in solution. The Tikhonov regularization method, which is a non-iterative stabilization technique, has been widely adopted for overcoming the ill-posed nature (or numerical instability). However, in this paper, we introduce an “iterative” regularization method, specifically, the iterated Tikhonov regularization method. The iterated method is applied to the present load determination problem. The result of the iterative method is compared with that of the (non-iterative) Tikhonov regularization. The rate of convergence for the introduced iterative method turned out to be very fast. The accuracy and applicability of the introduced method are examined through a numerical experiment.     

求解非线性动力学方程的错差迭代法

针对如何求解非线性动力学方程提出了一种错差迭代方法.首先待求系统须能表示成由线性齐次部分与非线性部分组成的一阶微分方程组的形式,然后以方程组所对应线性齐次系统的解析解作为初始解,代入一阶微分方程组的非线性部分,组成新的非齐次线性方程组,并求其解析解.以此解析解替代初始解,重复上述迭代过程以求得满足要求的系统近似解.最后利用谐波函数或多项式函数对解进行数据拟合,得到形式简单易用的近似解.算例表明该算法的有效性和实用性.     

基于奇异值分解的压缩感知噪声信号重构算法

压缩感知是通过对信号信息采样的信号处理新方法,它对可压缩信号可以大大降低采样数据.为提高噪声信号在压缩感知中的重构精度,本文提出了一种基于对观测矩阵奇异值分解的噪声信号重构算法,该算法对随机观测矩阵进行奇异值分解,通过均值算法修改对角矩阵的特征值,产生新的观测矩阵用于线性测量,理论证明了新观测矩阵比原观测矩阵具有更高的重构精度.仿真结果表明,算法重构精度在一维信号提高了3％～5％,二维信号的PSNR值提高1～2 dB.     

测试系统中非平稳信号的时频优化小波包检测算法

非平稳信号为测试系统所测试分析的主要目标之一.对于这些信号传统的检测方法(例如:傅里叶变换)不能起到有效的分析作用.小波包变换是非平稳信号分析的常用工具.Shannon小波函数是现有的单小波家族中唯一能够对信号频域进行严格划分的小波函数,但是由于其时域的非紧支性限制了其应用.本文通过对Shannon小波函数的时频联合优化,改善了其在非平稳信号检测过程中的性能;首先在时域上,改写其时域表达式,并保留其频域的紧支性,提升了其时域的紧支性;其次在频域上,提出了对Shannon小波函数频域滤波器的插值算法,改善其频域的滤波性能;再次,通过牛顿插值法给出了算法的快速实现;最后,做出了仿真实例.结果表明,通过本文的算法,改善了Shannon小波包变换的性能,使其成为测试系统关于非平稳信号检测的有效手段.