Can a finite element method perform arbitrarily badly?

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the -norm and the nodal point errors converge arbitrarily slowly. With the -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.

     

基于经典小波变换的布里渊光时域反射计光信号处理

布里渊光时域反射计结构的布里渊散射分布式光纤传感器检测的是自发散射光,信号非常微弱,而且频带在几十兆赫兹以上,难以应用普通相干解调方法。针对传感散射光信号特点,提出基于经典(Morlet)小波变换的光相干检测方法。首先采用微波电光调制产生频移参考光和自发布里渊散射光进行相干检测,再应用经典小波变换进行散射光信号的幅度解调,得到信噪比改善的布里渊散射传感光信号。给出了数值模拟和实验数据处理结果,表明经典小波变换能较好地处理布里渊光时域反射计检测信号。并和基于希尔伯特(Hilbert)变换的传感信号处理方法进行了对比,发现此方法优于基于希尔伯特变换的信号处理。     

激光主动探测中回波信号的小波去噪方法

在分析激光主动探测中回波信号的噪声特性和小波变换去噪原理的基础上，提出了一种基于最大信噪比准则的小渡阈值去噪方法。首先用最大信噪比准则对小波变换系数进行阈值选取，然后采用软阂值方法对小波系数进行量化处理后再重构。仿真结果表明最大信噪比准则小波去噪方法改善信噪比效果十分显著，检测下限达到-16．2dB。证明了该方法在激光主动探测系统回波信号检测中的有效性。     

An effective noise removal technique for recovering the shapes of diamond abrasive grains in SLM images degraded by clustered spike noise

A new noise-removal technique is applied to scanning laser microscopic (SLM) images to remove clustered spike noise in the images and to recover the shapes of diamond abrasive grains degraded by the noise. For achievement of this purpose, noise points in the SLM image are accurately detected by taking advantage of their properties in the space and spatial-frequency regions. The noise points are removed by a method of smoothing that is based on linear interpolation; that is, their pixel values are replaced by the interpolated values of their non-noise neighboring points. Noise-point information in the space region is acquired from image segmentation based on pixel classification, while noise-point information in the frequency region is derived from redundant wavelet decomposition for the SLM image. Fisher's linear discriminant method is used to yield the two noise-point images. The degraded grain shapes in the SLM images at different noise levels are satisfactorily recovered with a single iteration of smoothing without losses in sharp edges although a single smoothing needed four interpolations. Thus, the present noise-removal technique is shown to be effective for recovering the original shapes of the grains in every SLM image.     

Phase recovery from fringe patterns using the continuous wavelet transform

Interferometry is well established as an optical technique in which a measurand is encoded as the phase of a periodically varying intensity pattern. In view of the inherent accuracy of interferometry, many methods have been developed to retrieve the phase from images of the fringe pattern. Our focus in this paper is one such technique—the continuous wavelet transform (CWT). We begin by reviewing the CWT and the space–spatial–frequency localisation properties of wavelets. We show that a path which follows the maximum modulus of the CWT (the wavelet ridge) gives the instantaneous fringe frequency as a function of spatial displacement. The phase is automatically and trivially obtained, without discontinuities, by integration. Examples of practical wavelets are given and algorithms to isolate the wavelet ridge reviewed.     

基于三角小波的弹性薄板高精度分析方法

采用同时具有三角函数良好逼近特性和小波多分辨率与局部特性的Hermite插值型三角小波,基于二维张量积三角小波,推导了求解各种不同边界条件下的矩形弹性薄板的弯曲、振动和屈曲问题的统一列式,同时给出了两种提高计算精度的方法一升阶法和多分辨率法。数值算例表明,三角小波法求解弹性薄板的弯曲、振动和屈曲问题时,能方便地处理各类边界条件,计算效果良好;自振特性分析更具优势,升阶法和多分辨率法能有效地提高分析精度。     

Convergence of Riemannian sums of inverse wavelet transforms

We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones.     

Nonlinear analysis of a structure loaded by a stochastic excitation

For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.     

医学数字化CT图像压缩效果的统计分析与评价

为探讨医学数字化CT图像的压缩效果,选取具有重要临床意义的肺部CT数字化图像2186张,基于小波变换进行无视觉损失压缩,对压缩效果进行统计分析与评价。经肺部影像学专家肉眼进行盲法评判,压缩后与病理诊断结果符合率为91.89(95%C I为:79%-98%),压缩前后综合评分差别无统计学意义。小波变换较好地实现了对肺部患者数字化CT图像的无视觉损失压缩。