小波变换软阈值去噪在粗晶材料超声检测中的应用

本研究多尺度小波分析方法在粗晶材料超声检测信号增强中的应用。在分析结构噪声，电噪声和缺陷信号的小波变换特性的基础上，提出一种用一个尺度间变化的门限闭值来抑制噪声的小波变换系数，并以各尺度缺陷信号的能量关系形成权值，加权重构信号来提高信噪比。实验结果表明，该方法具有很好的去噪效果，增强了粗晶材料缺陷的检出率。     

Wavelet expansions forBMOρ (w)‐functions

We give necessary and sufficient conditions on the wavelet coefficients of a function for being a member of some BMO_φ (w) space. We achieve this characterization for a wide variety of wavelet systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于线性回归模型的有偏估计

有偏估计方法是近代回归分析的常用方法．本文研究了几种常用的有偏估计方法，澄清了这些方法的区别和联系．对有偏估计的一些关键点进行研究，给出了一种新的岭参数确定法和一种新的主成分概念，并讨论了这些方法的优良性．为了提高有偏估计的效率，提出了用比例因子规范模型的方法．最后，给出了说明本文方法的数值例子．     

Wavelet transforms and order-two densities of fractals

We highlight a correspondence between order-two densities and wavelet-like transforms of certain fractal measures. We use a variant of the ergodic theorem to demonstrate that these densities and transforms are well-behaved for a large class of quasi-self-similar fractals. We show that parallel ideas can be used to study the local behavior of certain fractal functions.     

Some recent and new results on the maximum entropy distribution

This letter concerns the maximum entropy (ME) distribution proposed by Theil and Laitinen (1980); it summarizes some of the results obtained with this distribution and its explores the conditioning of the ME covariance matrix as the number of variables increases.     

Low-pass filters and representations of the Baumslag Solitar group

We analyze representations of the Baumslag Solitar group

that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.

     

"Push-the-Error" Algorithm for Nonlinear n-Term Approximation

This paper is concerned with further developing and refining the analysis of a recent algorithmic paradigm for nonlinear approximation, termed the "Push-the-Error" scheme. It is especially designed to deal with L_∞-approximation in a multilevel framework. The original version is extended considerably to cover all commonly used multiresolution frameworks. The main conceptually new result is the proof of the quasi-semi-additivity of the functional N(ε) counting the number of terms needed to achieve accuracy ε. This allows one to show that the improved scheme captures all rates of best n-term approximation.     

Optical wavelet de-noising applied in multi-span nonlinear fiber links

In this work, optical wavelet de-noising with several different types of wavelets such as db4, coif4 and dmey wavelet was applied at the end of the 40 Gbit/s multi-span intensity-modulated fiber communication systems. The results of numerical simulations carried out in different fiber links demonstrated that the optical wavelet de-noising method could remove the random amplitude fluctuation induced by the interaction of EDFA’s ASE noise and optical fiber’s dispersion and nonlinearity. The SNR and BER curves of the optical bit sequence without and with optical wavelet de-noising in dispersion compensation fiber link were plotted to show the effectiveness of the wavelet de-noising in the fiber-optic communication systems and wavelet de-noising with demy wavelet can achieve better result than with other type wavelet.     

Modification of three dimensional topography of the machined KDP crystal surface using wavelet analysis method

The wavelet analysis method has been extensively employed to analyze the surface structures and evaluate the surface roughness. In this work, however, the wavelet analysis method was introduced to decompose and reconstruct the sampled surface profile signals in the cutting direction that achieved by SPDT (single point diamond turning) operation, and the surface profile signals in tool feeding direction were reconstructed with the approximate harmonic functions directly. And moreover, the orthogonal design method, i.e. the combination design of general rotary method, was resorted to model the variations of the independent frequency and amplitude of different simulated harmonic signals in the cutting and tool feeding directions. As expected resultantly, a novel 3D surface topography modeling solution was established, which aims to predict and modify the finished KDP (potassium dihydrogen phosphate or KH₂PO₄) crystal surfaces. The validation tests were carried out finally under different cutting conditions, and the collected average surface roughness in any case was compared with the corresponding value as predicted. The results indicated the experimental data were well consistent with the predictions, and only an average relative error of 11.4% occurred in predicting the average surface roughness.     

Wavelet expansions and asymptotic behavior of distributions

We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S₀(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients.