CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel

In this paper, a computational method for numerical solution of a class of integro-differential equations with a weakly singular kernel of fractional order which is based on Cos and Sin (CAS) wavelets and block pulse functions is introduced. Approximation of the arbitrary order weakly singular integral is also obtained. The fractional integro-differential equations with weakly singular kernel are transformed into a system of algebraic equations by using the operational matrix of fractional integration of CAS wavelets. The error analysis of CAS wavelets is given. Finally, the results of some numerical examples support the validity and applicability of the approach.     

基于小波变换的开都河径流量多时间尺度分析

以开都河大山口站1956—2006年的年径流量资料为例,利用Morlet小波变换对其水文序列的多时间尺度演变特性进行了分析,并预测了开都河2006年以后的年径流量变化趋势。结果表明:开都河存在6 a、10 a、15 a和38 a等4个主周期,其中38 a和10 a分别为第一和第二主周期;2006年后的未来几年内开都河将处于偏枯期。     

基于小波分析的丹江口水库水文年度入库径流变化特征

根据丹江口水库运行调度的实践,采用Morlet小波函数,对丹江口水库水文年度、汛期和非汛期的径流时间序列进行小波分析,揭示了丹江口水库入库径流多时间尺度的复杂结构,并分析了不同尺度下径流序列的周期变化和突变点。研究结果表明：水文年度、汛期、非汛期入库径流序列都存在9,20,40,50a的主要周期,并且水文年度入库径流与汛期径流具有相似的周期演变特征。研究成果可供丹江口水库运行调度参考。     

基于小波的曲线任意放大

文章利用小波多分辨理论,提出了任意比例放大曲线的方法.该算法简单,放大后的曲线失真小且比较光滑.同时,在理论上讨论了适于放大缩小曲线的小波基应具有的特征.理论和实验结果均说明双正交B样条小波和半正交B样条小波具有较好的几何特征,适于本文算法.     

基于DSP的嵌入式零树编码算法设计

本文结合TI公司DM642的结构特点及EZW算法原理,提出了运用DSP实现图像压缩系统的设计方案。为了提高算法效率,文中用提升小波算法代替原EZW算法中的传统小波（mallat）变换算法。实验结果表明达到较为满意的效果。     

Rational wavelet decompositions of transfer functions in hardy-sobolev classes

The model approximation of transfer functions using rational wavelets (or molecular decompositions) is considered. By using techniques from Hardy-Sobolev spaces it is shown that Hilbert space methods such as a modified matching-pursuit algorithm and least-squares technique can be employed to obtain good approximations in bothH ² andH norms. Several theoretical results are given on rates of convergence when the methods are applied to delay systems and fractional filters.The research of the first author was supported by E.P.S.R.C.     

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper, an Automated Brain Image Analysis (ABIA) system that classifies the Magnetic Resonance Imaging (MRI) of human brain is presented. The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis. The Non-Subsampled Shearlet Transform (NSST) that captures more visual information than conventional wavelet transforms is employed for feature extraction. As the feature space of NSST is very high, a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies. A combination of features that includes Gray Level Co-occurrence Matrix (GLCM) based features, Histograms of Positive Shearlet Coefficients (HPSC), and Histograms of Negative Shearlet Coefficients (HNSC) are estimated. The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers; k-Nearest Neighbor (kNN), Naive Bayes (NB) and Support Vector Machine (SVM) classifiers. The output of individual trained classifiers for a testing input is hybridized to take a final decision. The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data (REMBRANDT) database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.     

基于Gabor小波变换的人脸表情识别技术研究

为了使人机交互得到更好的研究,提出了一种基于Gabor小波变换的人脸表情识别的新方法;首先对图像进行预处理以提高后续处理的准确度,预处理包括确定纯的人脸表情区域,尺寸和灰度归一化,然后对表情子区域进行Gabor小波变换,提取表情特征矢量,进而构建表情弹性图,最后用模板匹配的方法来识别图像的人脸表情;经过实验,发现Gabor小波变换提取特征时受光照影响比较小,该系统不仅具有很好的鲁棒性,并且速度快,识别率高。     

RCS测量数据的Morlet小波消噪方法研究

为了消除外界环境以及杂波和噪声对RCS测量精度的影响,提出了RCS测量数据的小波消噪方法,给出了小波消噪方法的具体步骤和实验结果.从实验结果可以看出,小波消噪方法能够对信号中的有用部分和噪声进行有效分离,使得信噪比及测量精度得到提高.     

Simultaneous speckle reduction and contrast enhancement for ultrasound images: Wavelet versus Laplacian pyramid

Speckle can be described as random multiplicative noise. It hampers the perception and extraction of fine details in the image. Speckle reduction techniques are applied to ultrasound images in order to reduce the noise level and improve the visual quality for better diagnoses. It is also used as preliminary treatment before segmentation and classification. Several methods have been proposed for speckle reduction in ultrasound images. Multiscale contrast enhancement has proven to be very efficient for x-ray images. A recent study by Dippel et al. doing a comparison, contrast enhancement of radiographs (x-ray and mammography), between the Laplacian pyramid and the wavelet one proves that the Laplacian pyramid method gives a better result than the wavelet one; the filtering aspect was not taken into account. In ultrasound images a strong contrast variation exists which is different from x-ray and mammography. In this paper a wavelet pyramid with simultaneous speckle reduction and contrast enhancement was applied for the first time on ultrasound images with the area of interest and compared to a Laplacian enhancement pyramid. The optimum choice of wavelet bases for ultrasound images is investigated in this study. In order to realize a fair comparison, the same nonlinear modification in both multiscale schemes is used. The comparison proves that the wavelet pyramid gives a much better result than the Laplacian one for simultaneous speckle reduction and contrast enhancement of ultrasound images. The text was submitted by the author in English. Ali Samir Saad, 1964. 1996 PhD in image processing, Polytechnics School of the Engineering University of Nantes, France. 1993 Masters in Electronics. 1990 Masters in Digital Image Processing, Institute of Computer Sciences and Communication University of Rennes, France. 1989 BS in Electrical Engineering, University of Saint-Etienne. Academy of Lyon, France. 1996–2000 Research associate at the National Center for Macromolecular Imaging. Baylor, Houston, Texas. Assistant professor at King Saud University, Dept. of Biomedical Technology. Area of research in medical image processing and analysis, 23 publications, member of the American Association for the Advancement of Sciences. Marquis Who’s Who in the World; Cambridge Blue Book 2006.