用正交多小波压制地震信号的随机噪声

正交多小波可同时具有短支集、对称性或反对称性和正交性,这是一般的正交单小波所没有的性质,因而在处理信号时能取得更好的效果。本文详细说明了应用GHM正交多小波对地震信号进行去噪处理的原理,并给出实际例子说明该方法的有效性。     

两种子波用于1／f噪声相似性分析比较

应用样条子波和Daubechies子波分别对高斯白噪声和4种不同类型的1/f噪声信号进行了相似性分析,对比了分析结果。两种子波在对1/f信号进行相似性分析时,定性结果是一致的;在定量分析中,样条子波优于daubechies子波。     

Mallat算法在图像处理中的约束条件

指出了应用Mallat算法进行图像处理时容易出现的一些容易混淆和错误的问题,给出了正确使用Mallat算法的约束条件,用Haar和Daubechies小波研究了基于子带编码的图像压缩问题,给出了三种小波压缩编码方案并进行了基于约束条件的仿真实验,仿真结论可以启发我们构建有效的图像压缩编码方案和正确地应用Mallat算法.     

离散小波分析导论（一）：小波变换的基本思想,展缩方程,展缩小波

介绍了离散小波分析的基本理论，详细阐述了离散小波变换的实现方法，并指出离散小波变换的一些应用前景。     

Particles Spreading Phenomena in the Case of Glass Thermal Spraying

The spreading phenomena of particles during thermal spraying are quite difficult to observe given the kinetics of the process. In this work, the splat formation of glass and alumina is theoretically compared, showing that glass transition and low-thermal conductivity yield a higher ratio between cooling and flattening times, which strongly modifies their spreading behavior. Wipe tests show that splash—splat transition temperature can be modified by the glass composition and its subsequent hydrodynamic properties. The detection of peculiar remaining objects, such as fibers and wavelets shows the possibility of “freezing” some phenomena that are totally unobservable with crystalline oxides, except with high-velocity observations.     

广义齐型Besov范数约束下的图像分解

为了将图像分解为分片光滑的结构部分和振荡部分,提出一种新的变分图像分解模型.该模型利用第二代曲波和局部余弦基分别表征含噪图像中的结构分量和纹理分量,并采用全变差半范约束分片光滑部分的结构性;同时利用 Meyer 所建议的广义齐型 Besov 范数对噪声分量进行约束;最后利用基追踪去噪算法对新模型进行迭代求解.理论分析和实验结果表明,该算法对噪声具有较强的鲁棒性,并使边缘和细小的纹理信息保持稳定.     

A composite numerical scheme for the numerical simulation of coupled Burgers’ equation

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets leads to a system of linear equations and is solved using Matlab7.0. Convergence analysis of proposed scheme exhibits that the error bound is inversely proportional to the resolution level of the Haar wavelet. Finally, the adaptability of proposed scheme is demonstrated by numerical experiments and shows that the present composite scheme offers better accuracy in comparison with other existing numerical methods.     

小波分析在三维地形数据简化中的应用研究

研究了小波分析在三维地形数据简化中的应用。在分析了小波多分辨率分析理论的基础上,重点探讨了小波多分辨率分析理论在三维地形简化中的应用,提出了实现三维地形数据简化的一种新的方法。     

A generalization of frame perturbation in Hilbert subspaces and its application to wavelet subspaces

A perturbation theorem for frames in a Hilbert space is obtained, which is a generalization of a result by Christensen. Based on this general result, an irregular sampling theorem for frames in wavelet subspaces is established, which has a previous result as a special case.     

Efficient algorithms to compute Hankel transforms using wavelets

The aim of the paper is to propose two efficient algorithms for the numerical evaluation of Hankel transform of order ν, ν>−1 using Legendre and rationalized Haar (RH) wavelets. The philosophy behind the algorithms is to replace the part xf(x) of the integrand by its wavelet decomposition obtained by using Legendre wavelets for the first algorithm and RH wavelets for the second one, thus representing Fν(y) as a Fourier-Bessel series with coefficients depending strongly on the input function xf(x) in both the cases. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithms.