Genetic algorithms based on wavelet transform for resolving simulated overlapped spectra

Wavelet transform-based genetic algorithms are proposed for resolving simulated overlapped spectra. Wavelet transform as a derivative method is used for de-noising, for deducting background absorption as well as for peak finding in order to get an estimation of parameters of unresolved spectra. Then genetic algorithms, using the estimations of parameters as input values, are employed to resolve unresolved bands. As a consequence, a good optimized solution was achieved since the reliable estimation of initial values can greatly facilitate the convergence of genetic algorithms and the calculation time is shortened accordingly.     

Wavelet packets associated with nonuniform multiresolution analyses

A multiresolution analysis was defined by Gabardo and Nashed for which the translation set is a discrete set which is not a group. We construct the associated wavelet packets for such an MRA. Further, from the collection of dilations and translations of the wavelet packets, we characterize the subcollections which form orthonormal bases for L²(R).     

The necessary condition and sufficient conditions for wavelet frame on local fields

In the paper entitled “Multiresolution analysis on local fields” [H.K. Jiang, D.F. Li, N. Jin, Multiresolution analysis on local fields, J. Math. Anal. Appl. 294 (2) (2004) 523-532], we establish the orthonormal wavelet construction from multiresolution analysis on local fields. The objective of this paper is to construct wavelet frame on local fields. A necessary condition and four sufficient conditions for wavelet frame on local fields are given. An example is presented at the end.     

Two-index Clifford-Hermite polynomials with applications in wavelet analysis

Clifford analysis may be regarded as a higher-dimensional analogue of the theory of holomorphic functions in the complex plane. It has proven to be an appropriate framework for higher-dimensional continuous wavelet transforms, based on specific types of multi-dimensional orthogonal polynomials, such as the Clifford-Hermite polynomials, which form the building blocks for so-called Clifford-Hermite wavelets, offering a refinement of the traditional Marr wavelets. In this paper, a generalization of the Clifford-Hermite polynomials to a two-parameter family is obtained by taking the double monogenic extension of a modulated Gaussian, i.e. the classical Morlet wavelet. The eventual goal being the construction of new Clifford wavelets refining the Morlet wavelet, we first investigate the properties of the underlying polynomials.     

An image adaptive, wavelet-based watermarking of digital images

In digital management, multimedia content and data can easily be used in an illegal way—being copied, modified and distributed again. Copyright protection, intellectual and material rights protection for authors, owners, buyers, distributors and the authenticity of content are crucial factors in solving an urgent and real problem. In such scenario digital watermark techniques are emerging as a valid solution. In this paper, we describe an algorithm—called WM2.0—for an invisible watermark: private, strong, wavelet-based and developed for digital images protection and authenticity. Using discrete wavelet transform (DWT) is motivated by good time-frequency features and well-matching with human visual system directives. These two combined elements are important in building an invisible and robust watermark. WM2.0 works on a dual scheme: watermark embedding and watermark detection. The watermark is embedded into high frequency DWT components of a specific sub-image and it is calculated in correlation with the image features and statistic properties. Watermark detection applies a re-synchronization between the original and watermarked image. The correlation between the watermarked DWT coefficients and the watermark signal is calculated according to the Neyman–Pearson statistic criterion. Experimentation on a large set of different images has shown to be resistant against geometric, filtering and StirMark attacks with a low rate of false alarm.     

傅立叶变换与小波变换的比较教学

本文针对小波变换教学中小流变换概念理解困难的问题，提出了一种比较教学方法，通过分析小波变换与傅立叶变换之间的联系，并从四个方面进行对比，清楚地描述了小波变换的本质，从而对加深对小波变换的理解。     

Wavelets and Elman Neural Networks for monitoring environmental variables

An application in cultural heritage is introduced. Wavelet decomposition and Neural Networks like virtual sensors are jointly used to simulate physical and chemical measurements in specific locations of a monument. Virtual sensors, suitably trained and tested, can substitute real sensors in monitoring the monument surface quality, while the real ones should be installed for a long time and at high costs. The application of the wavelet decomposition to the environmental data series allows getting the treatment of underlying temporal structure at low frequencies. Consequently a separate training of suitable Elman Neural Networks for high/low components can be performed, thus improving the networks convergence in learning time and measurement accuracy in working time.     

扩散系数小波估计的强相合性

本文研究了一维扩散方程中扩散系数的非参数估计,给出了有界Lipschitz扩散系数的线性小波估计,证明了所得估计量的强相合性.     

基于叶片光学属性的作物叶片水分含量反演模型研究

叶片含水量是反映作物生理特性的一个重要参数,对生态环境的研究具有重要意义。采用小波分析方法,分析叶片含水量对反射率的影响特征,建立综合利用多波段信息的作物叶片水分含量反演模型。基于PROSPECT模型的辐射传输理论,推导出由叶片反射率光谱的小波系数反演叶片水分含量C_W的理论模型。利用六种常用的小波函数,对叶片组分水、干物质和白化基本层的吸收光谱进行小波分解。选取对水分变化最敏感,同时对其他组分不敏感的分解尺度和波段位置,找到能稳定突出水的光谱特征的小波系数。结果表明：bior1.5小波函数在尺度为200 nm,波段位置为1 405和1 488 nm的小波系数具有上述特征。建立由叶片反射率光谱的bior1.5小波系数反演叶片水分含量C_W的反演模型,模型有两个转换系数a和Δ都受叶片结构参数N的影响。利用PROSPECT模型生成模拟光谱数据集,校正建立的叶片水分含量反演模型中的两个转换系数a和Δ,并与LOPEX93实验光谱数据集结合验证反演模型。结果表明：反演模型不仅比传统基于植被指数的统计模型在精度上有提高(反演值与实测值的R2最高达到0.987),而且更加稳定,普适性更高。研究表明,小波分析方法在利用高光谱数据反演作物叶片水分含量方面具有独特的优势。