Regularity criteria for almost every function in Sobolev spaces

In this paper we determine the multifractal nature of almost every function (in the prevalence setting) in a given Sobolev or Besov space according to different regularity exponents. These regularity criteria are based on local Lp regularity or on wavelet coefficients and give a precise information on pointwise behavior.     

Wavelet-based morphological correlation

A wavelet-based morphological correlation (WBMC) is proposed as a new architecture to improve the properties of the classical morphological correlation (MC). For the WBMC, a dilated wavelet intensity function is introduced to filter the joint power spectrum (JPS) of the MC before final inverse Fourier transform. Computer simulation results show that, as compared with the linear correlation (LC), the conventional MC and the joint wavelet transform correlation (JWTC), the WBMC provides better discrimination capability with sharp and unmistakable correlation signal and its performance metrics are more stable under input outlier noise (salt-and-pepper noise). Although the WBMC loses illumination-invariance when input illumination factor is larger than unity, considerable discrimination capability is still maintained.     

Two analyte calibrations from the transient response of a single potentiometric sensor employed with the SIA technique

Simultaneous quantification of Cd²⁺ and Pb²⁺ in solution has been correctly targeted using the kinetic information from a single non-specific potentiometric sensor. Dual quantification was accomplished from the complex information in the transient response of an electrode used in a Sequential Injection Analysis (SIA) system and recorded after step injection of sample. Data was firstly preprocessed with the Discrete Wavelet Transform (DWT) to extract significant features and then fed into an Artificial Neural Network (ANN) for building the calibration model. DWT stage was optimized regarding the wavelet function and decomposition level, while the ANN stage was optimized on its structure. To simultaneously corroborate the effectiveness of the approach, two different potentiometric sensors were used as study case, one using a glass selective to Cd²⁺ and another a PVC membrane selective to Pb²⁺.     

A WAVELET TRANSFORM AND ITS APPLICATION TO SPECTROSCOPIC ANALYSIS

ABSTRACT

An introduction to the wavelet transform and its applications in spectroscopy analysis are presented. Owing to the property of the dual localization both in time and in frequency domains, the wavelet transform exhibits several useful characteristics. With the wavelet transform a signal can be decomposed into series of contributions according to the frequency difference, these contributions are respectively called discrete approximations and discrete details. By applying certain treatment to the discrete approximations (the low frequency part) or the discrete details (the high frequency part), a part of the original signal within a certain frequency range can be obtained. The wavelet transform has been applied in various fields of the analytical chemistry, including removal of high frequency noise, information extraction, resolution of overlapping signals, and data compression etc. Research concerning application in analytical chemistry are introduced in respect of photoacoustic spectroscopy, EXAFS spectrum, NMR analysis, and Raman spectrum.     

小波域局部维纳滤波器估计误差分析及图像去噪

对小波域局部维纳滤波算法的估计误差进行了理论分析,推导了估计误差平方期望表达式,得到了一种观测系数局部方差估计的阈值.以此为基础,提出了一种小波域图像去噪算法.先对观测系数做阈值化处理,再进行局部自适应维纳滤波.实验结果表明,该方法提高了真实信号系数方差估计的准确度,在去噪性能上优于Mihcak等提出的LAWML算法.     

小波分析在气泡幕散射光信号处理中的应用

选取Daubechies小波对尾流气泡幕散射光信号做一维离散小波变换,小波阶数为3,尺度数Level为5,得到了原始信号的小波分析和重构误差结果.经db3小波分解,散射光信号的低频及高频部分区别不大,可能是信号采集频率过低(×10－1 s)导致的结果.对原始信号进行小波分析容易得到均值、中值、模式、标准差等统计量.通过对散射光信号进行一维平稳小波去噪、小波变换密度估计、小波系数选取等方面的分析,揭示了不同压强下散射光信号具有不同的性质.     

基于小波分析的气泡光散射空间谱强度分布的高斯拟合算法优化

将小波消噪方法应用在采用CCD器件作为光传感器的尾流气泡光散射空间谱强度分布检测技术中, 发现CCD输出经过消噪后的高斯拟合曲线比其直接进行高斯拟合的结果更逼近实际的气泡光散射谱强度分布,可以有效减小测量误差,使高斯拟合算法得以优化,从而解决了CCD饱和与测量噪音对散射谱强度分布半值宽度和峰值的影响,提高了用气泡光散射谱强度分布判断水中气泡存在和气泡大小的准确度.     

时变软阈值法在纳秒脉冲信号去噪中的应用

 对工程上常用的几种小波进行了分析,通过比较选定双正交小波为纳秒脉冲信号分析的母波,根据纳秒脉冲放电时产生的电磁干扰的特点提出基于多尺度分析的时变软阈值法,并对纳秒脉冲信号进行去噪处理。用Matlab自带的doppler波形和方波发生器产生的上升沿小于1 ns的方波对此方法进行检验,结果表明时变软阈值法明显优于传统的固定软阈值法。     

天体光谱信号去噪的小波域复合阈值新算法

利用谱线和噪声在小波域内的不同相关特性,提出了一种小波域复合阈值去噪算法。首先将小波系数作NeighShrink阈值处理,然后对得到的小波系数进行二值化,在此基础上定义了每一小波系数所对应的横向相关性指数和纵向相关性指数,最后确定出决定小波系数取舍的决策系数。由于该决策系数是通过多重判据得到的,因此该方法克服了简单阈值方法过保留或过扼杀的缺点,同时可以去除大脉冲噪声,实验结果表明了该方法的有效性。     

A finite wavelet domain method for wave propagation analysis in thick laminated composite and sandwich plates

An efficient numerical method is developed for the simulation of three dimensional transient dynamic response in thick laminated composite and sandwich plate structures involving very high frequencies and wave numbers. The proposed method incorporates Daubechies wavelet scaling functions for the interpolation of the in-plane displacements with a Galerkin formulation. It further explores the orthonormality and compact support of wavelet scaling functions to produce near diagonal consistent mass matrices and banded stiffness matrices. Hence, an uncoupled equivalent discrete spatial dynamic system is formulated, synthesized and rapidly solved in the wavelet domain using an explicit time integration scheme. The in-plane wavelet interpolation is further combined with an efficient high order layerwise laminate plate theory, that implements Hermite cubic splines for the through-the-thickness approximation of displacement fields. Numerical results are presented on the prediction of guided waves in laminated and thick sandwich composite plates and compared with respective solutions obtained by analytical, semi-analytical and time domain spectral element models. The method yielded higher convergence rates and substantial reductions in computational effort compared to respective time domain spectral finite elements.