A multiresolution homogenization of modal analysis with application to layered media

We apply multiresolution techniques to study the effective properties of boundary value problems. Conditions under which boundary values are preserved in the effective (‘homogenized') formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic formulation and those of the effective formulation are explored. Applications to the construction of effective Green function in a complex lamination are discussed. The analytic results are demonstrated via numerical computations.     

一种彩色视频图像序列的三维小波变换编码方法

该文给出了一种基于三维小波变换的彩色视频图像序列的编码方法。先将彩色视频图像序列的RGB(红绿蓝)色彩表示转换成YCbCr(亮度色度色度)表示,再将表示帧序的t坐标代换成z坐标,可将其看成是三维空间中的体。将其分成子块后,仿照二维图像小波变换的方法,对每个亮度色度分量做三维小波变换。变换后的各亮度色度分量的能量主要集中于低频波段,这些波段对该视频图像序列的视觉效果影响最大。将不同分量的各个不同波段按不同的精度量化并进行熵编码,可以达到去除帧内和帧间冗余,压缩数据的目的。试验表明,使用本方法可以达到较好的压缩效果。此方法较直观,速度也比较快。     

THE POISSON WAVELET TRANSFORM

This paper introduces a family of wavelet transforms based on the Poisson Transform. The wavelet transform maps L² (R)functions to a space described by two continuous variables, scale and translation, as well as a discrete index. Reconstruction in the wavelet domain can be done for each of the discrete indices. Additionally, a different reconstruction formula exists for the Poisson Transform domain. We develop the Poisson Wavelet Transform, present an example relevant to stable, over-damped, linear, time-invariant systems, and show the relationship between the Poisson Transform and the Poisson Wavelet Transform.     

Methodologies used for evaluation of video tools and algorithms in MPEG-4

MPEG-4 issued two calls for proposals requesting submission of algorithms and tools relevant to standardization of MPEG-4. This paper reports on the evaluation of tools submitted for evaluation in November 1995 and January 1996. Complete video coding schemes submitted in January 1996 are also covered. The goal of the evaluation was to cluster the tools according to the technical areas they address, to evaluate them according to the issues relevant to the standardization process, and finally to suggest areas of core experiments to improve a video verification model (VM) as soon as the VM becomes available. Altogether, MPEG evaluated 87 tools and 19 complete coding algorithms, most of them highlighted in this paper. During the evaluation, 19 areas for core experiments were identified. Each core experiment is targeted at different functionalities like compression efficiency, content-based coding, error resilience, scalability. This definition of core experiments caused close collaboration and supported mutual fertilization between organizations working on similar tools, which allowed the VM to progress much faster than expected.     

Wavelet-Based Synthesis of the Multifractional Brownian Motion

The multifractional Brownian motion （mBm） is introduced as a natural extension of traditional fractional Brownian motion （fBm）. The selling point of mBm is that its Hǒlder regularity is allowed to vary from point to point, such that makes it a promising model for those stochastic processes whose regularity evolves in time. A wavelet-based algorithm to synthesize a realization of mBm is proposed in this work. The desired local regularity of the multifractional process is obtained by controlling the weights of the wavelet expansion of the Gaussian white noise. This approach is not only time saving, also appro-priate for generating the multifractional process that is non-Gaussian and autocovariance function unknown in ad- vance. The validity is verified by numerical experiments and real-world data.     

A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory

A study of bending deformations of sandwich plates using a layerwise theory of laminated or sandwich plates is presented. The analysis is based on a wavelet collocation technique to produce highly accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed.     

评价机械加工表面形貌的小波变换方法

提出了用小波变换计算粗糙表面分形维数的新方法 ,并基于Weierstrass -Mandelbrot函数 (W -M函数Majumdar-Bhushan函数 (M -B函数 )对该方法进行了验证 ,结果表明该方法具有很高的计算精度。应用小波变换方法对核态池沸腾试验板表面形貌的分形特征进行了评价 ,包括铜和不锈钢材料 ,轧制、砂纸打磨和表面机械抛光等 3种加工方法生成 5个粗糙度级别的试验板 ,研究结果表明该方法能有效评价表面形貌的分形特征。     

基于小波算法的二阶线性定常分布参数系统的辨识

本文基于正交函数逼近方法,借助于小波变换,并利用其运算矩阵及其运算性质,研究了分布参数系统的辨识问题。将Haar小波正交基应用于分布参数系统的辨识中,经正交小波逼近变换,将原偏微分描述的分布参数系统转化为代数矩阵方程,并且,考虑了初始条件和边界条件,获得了算法简单、计算方便、具有较高精度的辨识算法,简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法。仿真实例表明了本文所提出的算法的有效性。     

Short term solar irradiance forecasting using a mixed wavelet neural network

In modern smart grids and deregulated electricity markets, accurate forecasting of solar irradiance is critical for determining the total energy generated by PV systems. We propose a mixed wavelet neural network (WNN) in this paper for short-term solar irradiance forecasting, with initial application in tropical Singapore. The key advantage of using wavelet transform (WT) based methods is the high signal compression ability of wavelets, making them suitable for modeling of nonstationary environmental parameters with high information content, such as short timescale solar irradiance. In this WNN, a combination of the commonly known Morlet and Mexican hat wavelets is used as the activation function for hidden-layer neurons of a feed forward artificial neural network (ANN). To demonstrate the effectiveness of the proposed approach, hourly predictions of solar irradiance, which is an aggregate sum of irradiance value observed using 25 sensors across Singapore, are considered. The forecasted results show that WNN delivers better prediction skill when compared with other forecasting techniques.     

Frequency domain image analysis for the characterization of porous products

Many pharmaceutical products are obtained via freeze-drying of liquid solutions to obtain stable long lasting preparations. The freeze-dry process produces porous cakes whose structure strongly depends on the freezing phase, so that monitoring and optimizing this phase can help both reducing the product cost and insuring its constant quality. Nowadays the optimization is usually performed by determining the cake mass transfer coefficient via a costly process in pilot plants, while the quality is assured only by controlling the process conditions. This paper describes an alternative way of approximately estimating the mass transfer coefficient, which is based on the observation of the product structure by a simple electron microscope followed by a frequency domain imaging process. While the process has been designed and characterized specifically for pharmaceutical products, the proposed approach can be used in several other fields where the characteristics of porous material have to be monitored.