Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

小波连通性研究进展

本文介绍了 L2(R)中一些特殊小波组成集在L2(R)中的拓扑几何性质——道路连通性,特别综述了近二十年来小波连通问题研究的主要进展并列出了一些悬而未决的问题,并简要说明了高维情形和其他情形的相应结果.     

基于离散小波变换的蛋白质结构、功能与进化关系延时交叉相关分析

基于氨基酸的疏水特性, 将离散小波变换与延时交叉相关分析相结合, 提出了一种分析蛋白质结构、功能和进化关系的新方法——序列小波层次相关法. 以丝氨酸蛋白酶超家族中Trypsin种属为研究对象, 描述了该方法在揭示不同物种的Trypsin蛋白质进化关系中的应用; 以蛋白质酪氨酸磷酸酶、血红蛋白和溶菌酶为例, 采用该方法揭示了蛋白质之间功能与序列的内在关系. 该方法为非参数方法, 具有简单、直观、可视和可操作性强等特点, 且不需要事先知道蛋白质的结构, 仅从蛋白质的氨基酸序列出发即可比较和揭示蛋白质之间的关系.     

小波变换轮廓术的测量范围研究

利用小波“脊”处的小波系数来提取变形条纹中的相位信息可以在很大程度上抑制条纹图中有用的基频分量与零频和其它谐波频率分量的混叠,弥补了傅里叶变换轮廓术的不足。从离散信号频域分析角度,推导了变形条纹小波变换的频谱描述形式,讨论了其测量范围,包括结构条件和抽样条件。结果表明,只有在无周期内瞬时频谱混叠,即任意位置处物体瞬时高度变化满足h/xx=b<1/3条件时,和不存在抽样引起的周期间瞬时频谱混叠的抽样条件下(即一个周期内的抽样点数m≥4时),小波变换轮廓术才能正确恢复被测物体的三维面型。计算机模拟和实验验证了该结论。     

简单有效的运动汽车投影阴影分割算法

在实时的车型识别系统中,由于光照的影响,需要一种简单快速有效的方法将汽车车体与其阴影分割开。利用阴影的光谱属性,同时根据阴影的几何特征及阴影区域内的点和汽车的空间位置、形状等相关特点,提出一种基于小波变换多分辨率特性的阴影分割算法,该算法能有效地分割出阴影与目标之间的分界线。先利用阴影的光谱属性对阴影进行粗分割,然后利用小波变换的多尺度性对候选阴影点进行特征提取,从而获取最后的阴影分界线。该方法不需要事先确定光源的方向、车体的彩色信息和背景纹理信息,能有效地分割任何颜色、任何背景纹理下、任何光源方向下的运动汽车投影阴影。实验表明,该方法定位准确,处理速度快,抗噪能力强,为进一步的车型识别提供基础。     

声纹的变压器放电与机械故障诊断研究

变压器中的一些放电和机械故障会产生异常声,可用于故障检测.据此,该文提出基于可听声的变压器放电和机械故障诊断方法.针对机械故障声与变压器本体噪声特征相似易混淆的问题,提出改进小波包-BP神经网络算法,与传统小波包-BP神经网络算法相比声音识别率提高了5.7％.为提高声音识别系统的泛化性,提出基于梅尔对数频谱和卷积神经网...     

提升小波变换与分形相结合的图像压缩

提出了一种提升小波变换与分形相结合的图像压缩方案.充分利用小波变换后系数能量的分布特性,对提升小波变换后的低频部分采用改进的分形图像压缩编码,其余部分采用集合分裂嵌入块(SPECK)编码算法.试验结果表明,该方法在提高了压缩效率的同时,获得了较高的恢复图像质量.     

自然地面背景下红外目标检测算法

为了快速准确地检测出以地面物体为背景的红外序列图像中的目标,结合小波变换的特点及其应用于图像边缘检测的优点,提出了一种基于小波技术的图像预处理算法。该方法利用图像边缘在目标识别中的重要作用,讨论了基于小波变换的图像边缘检测方法,并结合地面背景红外图像自身的特点,大大地提高了单帧的检测概率。     

微分Haar-Gaussian小波变换在大景深物体边缘测量中的应用

提出了微分Haar_Gaussian小波变换算法并将其应用于边缘检测,在空域和频域中进行变换,并应用带宽匹配方法和远心测量光学系统,提高了运算速度,通过对实际大景深物体离焦像的边缘测量,得到了准确的结果。     

Permutation Entropy-Based Interpretability of Convolutional Neural Network Models for Interictal EEG Discrimination of Subjects with Epileptic Seizures vs. Psychogenic Non-Epileptic Seizures

The differential diagnosis of epileptic seizures (ES) and psychogenic non-epileptic seizures (PNES) may be difficult, due to the lack of distinctive clinical features. The interictal electroencephalographic (EEG) signal may also be normal in patients with ES. Innovative diagnostic tools that exploit non-linear EEG analysis and deep learning (DL) could provide important support to physicians for clinical diagnosis. In this work, 18 patients with new-onset ES (12 males, 6 females) and 18 patients with video-recorded PNES (2 males, 16 females) with normal interictal EEG at visual inspection were enrolled. None of them was taking psychotropic drugs. A convolutional neural network (CNN) scheme using DL classification was designed to classify the two categories of subjects (ES vs. PNES). The proposed architecture performs an EEG time-frequency transformation and a classification step with a CNN. The CNN was able to classify the EEG recordings of subjects with ES vs. subjects with PNES with 94.4% accuracy. CNN provided high performance in the assigned binary classification when compared to standard learning algorithms (multi-layer perceptron, support vector machine, linear discriminant analysis and quadratic discriminant analysis). In order to interpret how the CNN achieved this performance, information theoretical analysis was carried out. Specifically, the permutation entropy (PE) of the feature maps was evaluated and compared in the two classes. The achieved results, although preliminary, encourage the use of these innovative techniques to support neurologists in early diagnoses.