基于高斯函数的小波系及其快速算法

系统地探讨了由高斯函数各阶导数所构成的小波系及其性质 ,计算表明其第n阶导数具有n阶消失矩 .文中以高斯函数为尺度函数 ,讨论了高通滤波器和低通滤波器的特殊关系 ,并给出了以高斯函数 1到 6阶导数作为小波时快速算法所需要的滤波器系数 .

Gaussian 小波系在求解N-S方程中的应用

利用Ｇａｕｓｓｉａｎ小波变换使Ｌａｐｌａｃｅ算子降价的性质对任意可变区域上的不可压Ｎ－Ｓ方程进行小波变换．在变换域上Ｎ－Ｓ方程变成了一阶波动方程，用特征线法进行首次积分，逆变换后得到物理空间中的积分方程．用算子方程理论讨论了该积分方程解的存在唯一性，并给出了保证解存在唯一的充分条件，得到了Ｎｅｕｍａｎｎ级数的形式解．

离散空间■~2(Z)中正交小波系的完备性

本文研究2(Z)中正交小波系的完备性,其主要目的是寻找一些容易验证的充分条件．为此,我们首先改进了Frazier的定理,给出小波系完备的一个刻画,然后在此基础上得到三个容易验证的充分条件．

用改进的多分辨小波网络辨识非线性动态系统

多分辨小波网络不便于处理非均匀分布样本和在线辨识非线性动态系统 ,对此提出了两点改进 :首先给出一种把非均匀分布样本近似到小波网格系上的方法 ;然后提出一种可变的小波网络及其学习方法 .最后用改进的小波网络辨识非线性动态系统 ,仿真结果验证了这种改进方法的可行性和有效性 .

信号处理中的小波分析

介绍了母小波和完全小波系的概念，详述了它们的数字特征。给出了连续小波变换、离散小波变换和二进离散小波变换的定义并参考Ｒ２空问的矢量表达式导出了它们的逆变换。

基于小波变换的高光谱图像消噪

本文主要针对高光谱图像的特点,利用波段间的几何信息高冗余性,通过小波分解去除高频的噪声和几何信息,保留低频的光谱信息。以其他波段的几何信息辅助噪声污染波段重构,经过相应的小波重构滤波器滤波,获得该波段图像的重建以进行消噪。

变截面涡旋盘双正交小波频谱表面降噪与重构

为了获取真实的变截面涡旋盘表面形貌特征信息,必须去除试样制备及数据采集过程中产生的噪声信号并进行形貌重构。利用Talysurf CLI1000三维形貌测量仪提取变截面涡旋盘两处试样的表面形貌数据,基于小波降噪理论,通过计算降噪前后表面信号的能量比PER、标准差ERR以及相关系数r等参数,选择双正交小波系bior6.8对表面形貌信号进行分层阈值降噪;结合频谱分析,分别对两处试样的表面数据进行分解,通过MATLAB仿真获得试样的重构表面形貌。计算两重构试样表面形貌的均方根误差RMSE分别为22.1907和38.0038,三维均方根粗糙度Sq分别降低了25%和22.47%,光滑度Sm分别提高了81.25%和46.04%。研究结果为变截面涡旋盘表面形貌有效降噪与准确重构提供了新的思路和方法,为进一步分析表面特征提供了条件。

一种基于HVS的小波域水印算法

将有意义的二值图像作为水印图像,运用Arnold变换进行置乱加密,结合人眼视觉系统特性(HVS),对载体图像小波系数进行计算以得到自适应的量化步长,以该步长对水平子带HL和垂直子带LH的小波系数进行量化,并把量化误差平均分配到这两个系数上,在保证嵌入强度的同时减少图像失真。水印提取时不需要原始载体图像和水印。实验结果证明本文提出的水印算法具有较好的不可见性和鲁棒性。

IMPROVEMENT ACCURACY OF SYSTEM IDENTIFICATION BASED ON MORLET WAVELET

A time frequency de-noising method is presented in the frequency response function （FRF） preprocessing based on the continuous wavelet transform. Morlet wavelet is employed to construct a filter bank to reduce the noise. The filter bank is a finite impulse response （FIR） linear phase filter thus maintaining phase consistency. A modified Morlet base function is proposed to meet the time frequency resolution by using transient excitation. Numerical simulation is conducted using a Group for Aeronautical Research and Technology in Europe （GARTEUR） aircraft model excited by the transient input. The white noise is added to the simulated data. Results show that the accuracy of the system identification is improved. The estimated error of the mode damping is decreased by 30% compared with that obtained from the noise-corrupted signal.

Fluorescence molecular imaging system and fusion algorithm based on 2CCD camera

Infrared and visible light images can be obtained simultaneously by building fluorescence imaging system,which includes fluorescence excitation,images acquisition,mechanical part,image transmission and processing section.This system studied the 2charge-coupled device(CCD)camera(AD-080CL)of the JAI company.Fusion algorithm of visible light and near infrared images was designed for the fluorescence imaging system with wavelet transform image fusion algorithm.In order to enhance the fluorescent moiety of the fusion image,the luminance value of the green component of the color image was changed.And using microsoft foundation classes(MFC)application architecture,the supporting software system was bulit in VS2010 environment.

Wavelet neural network based watermarking technology of 2D vector maps

A novel lossless information hiding algorithm based on wavelet neural network for digital vector maps is introduced. Wavelet coefficients being manipulated are embedded into a vector map, which could be restored by adjusting the weights of neurons in the designed neural network. When extracting the watermark extraction, those coefficients would be extracted by wavelet decomposition. With the trained multilayer feed forward neural network, the watermark would be obtained finally by measuring the weights of neurons. Experimental results show that the average error coding rate is only 6% for the proposed scheme and compared with other classical algorithms on the same tests, it is indicated that the proposed algorithm hashigher robustness, better invisibility and less loss on precision.

Filtering detecting signal of rockbolt with harmonic wavelet

Harmonic wavelets not only possess the traditional advantages of a wavelet function,they also have other merits such as clear expressions,more flexible time-frequency divisions,a simple transformation algorithm,a finer box-like frequency spectrum and others.Given the frequency distribution characteristics of the nondestructive testing signals from a rockbolt support system and based on the discrete harmonic wavelet transformation theory,we have effectively abstracted signals from frequency ranges concerned by removing useless high and low frequency signals from the testing signals of the rockbolt support system and obtained filtered signals with a reconstruction algorithm of harmonic wavelets.Finally,we applied the harmonic wavelet transformation in filtering analog signals and measured response signals of rockbolts.The results indicate that harmonic wavelets also have excellent filtering characteristics.

AN ADAPTIVE DIGITAL IMAGE WATERMARK ALGORITHM BASED ON GRAY-SCALE MORPHOLOGY

An adaptive digital image watermark algorithm with strong robustness based on gray-scale morphology is proposed in this paper.The embedded strategies include:The algorithm seeks and extracts adaptively the image strong texture regions.The algorithm maps the image strong texture region to the wavelet tree structures, and embeds adaptively watermark into the wavelet coefficients corresponding to the image's strong texture regions.According to the visual masking features, the algorithm adjusts adaptively the watermark-embedding intensity.Experimental results show the algorithm is robust to compression, filtering, noise as well as strong shear attacks.The algorithm is blind watermark scheme.The image strong texture region extraction method based on morphology in this algorithm is simple and effective and adaptive to various images.

Differentially Private Multidimensional Data Publication

Multidimensional data provides enormous opportunities in a variety of applications. Recent research has indicated the failure of existing sanitization techniques （e.g., k-anonymity） to provide rigorous privacy guarantees. Privacy- preserving multidimensional data publishing currently lacks a solid theoretical foundation. It is urgent to develop new techniques with provable privacy guarantees, e-Differential privacy is the only method that can provide such guarantees. In this paper, we propose a multidimensional data publishing scheme that ensures c-differential privacy while providing accurate results for query processing. The proposed solution applies nonstandard wavelet transforms on the raw multidimensional data and adds noise to guarantee c-differential privacy. Then, the scheme processes arbitrarily queries directly in the noisy wavelet- coefficient synopses of relational tables and expands the noisy wavelet coefficients back into noisy relational tuples until the end result of the query. Moreover, experimental results demonstrate the high accuracy and effectiveness of our approach.

An ECT System Based on Improved RBF Network and Adaptive Wavelet Image Enhancement for Solid/Gas Two-phase Flow

Electrical capacitance tomography(ECT) is a non-invasive imaging technique that aims at visualizing the cross-sectional permittivity distribution and phase distribution of solid/gas two-phase flow based on the measured capacitance.To solve the nonlinear and ill-posed inverse problem:image reconstruction of ECT system,this paper proposed a new image reconstruction method based on improved radial basis function(RBF) neural network combined with adaptive wavelet image enhancement.Firstly,an improved RBF network was applied to establish the mapping model between the reconstruction image pixels and the capacitance values measured.Then,for better image quality,adaptive wavelet image enhancement technique was emphatically analyzed and studied,which belongs to a space-frequency analysis method and is suitable for image feature-enhanced.Through multi-level wavelet decomposition,edge points of the image produced from RBF network can be determined based on the neighborhood property of each sub-band;noise distribution in the space-frequency domain can be estimated based on statistical characteristics;after that a self-adaptive edge enhancement gain can be constructed.Finally,the image is reconstructed with adjusting wavelet coefficients.In this paper,a 12-electrode ECT system and a pneumatic conveying platform were built up to verify this image reconstruction algorithm.Experimental results demonstrated that adaptive wavelet image enhancement technique effectively implemented edge detection and image enhancement,and the improved RBF network and adaptive wavelet image enhancement hybrid algorithm greatly improved the quality of reconstructed image of solid/gas two-phase flow [pulverized coal(PC)/air].

MULTI-SCALE GAUSSIAN PROCESSES MODEL

A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a linear basis that is composed of a scale function and its different translations. Finally the distribution of the targets of the given samples can be obtained at different scales. Compared with the standard Gaussian Processes (GP) model, the MGP model can control its complexity conveniently just by adjusting the scale pa-rameter. So it can trade-off the generalization ability and the empirical risk rapidly. Experiments verify the fea-sibility of the MGP model, and exhibit that its performance is superior to the GP model if appropriate scales are chosen.

Application of wavelet transform modulus maxima in boundary detection of potential fields

This study presents the use of the method of wavelet transform modulus maxima(WTMM) to detect boundaries of potential field sources.The boundaries of causative sources can be judged by calculating the local modulus maxima of wavelet coefficients at different scales.For the potential field data with noise,the detected boundaries at small scales are easy to be distorted by noise,however,at large scales,the noise can be suppressed greatly and presents more accurate boundary detection results.Therefore,we can get a better boundary judgment by considering the detected boundaries at all scales.Applying the WTMM method to synthetic models and a real data set of Meishan iron deposit,both get a good effect.

New reclosing scheme of distribution system for utilization of BESS using wavelet transform

This paper proposed the reclosing method in distribution system with battery energy storage system(BESS)using wavelet transform(WT).The proposed method performs the WT of load current and then calculates the absolute value of slope of detail coefficient.The mother wavelet used is db4of level6.The fault clearing is detected using the rapid increase of this value.After the detection of fault clearing,the reclosing is performed.To verify the proposed method,various simulations according to the fault clearing times,fault resistances,and fault lengths are performed using EMTP.The simulation results show that fault clearing can be detected using proposed absolute value of slope of detail coefficient and hence the reclosing can be performed successfully.

Decomposition in blocks at the level of wavelet coefficients and T（1 ） theorem on Hardy space

This paper deals with the establishment of \%T(1)\% theorem on Hardy space \%H 1\% under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo\|annular operator) on each block function (atom) are exactly analyzed to establish \%T(1)\% theorem on Hardy space.

Multi-Time Scale Analysis of Runoff at the Yangtze Estuary Based on the Morlet Wavelet Transform Method

Runoff series of the Yangtze River presents an intricate variation tendency under the reinforced influence of human activities.The Morlet Wavelet Transform method has been applied to analyze the annual runoff data from 1950 to 2011 at the Yangtze River Estuary.It can clearly reveal the multi-time scales structure,break point,change and distribution of periodic variation in the different time scales of the runoff series.The main conclusions are that:1) Repeated periodic oscillations accompanied by an extremely large fluctuation are presented in the runoff series with an obvious difference between wet and dry years,and the major periods of the time series are about 3,8,16 and 23 years respectively.Among them,the presented maximum periodic oscillation is 23 years scale.2) In the 23-year time scale,the wet periods are 1950-1958,1969-1980 and 1992-2003,and the dry periods are 1959-1968,1981-1991 and 2004-2011.3) It can be predicted from the view of long time scales that the low annual runoff will likely occur in the near future.