A class of symmetric wavelets and regularity analysis

Presents the generation of wavelet functions using the filter H(ω)=(1+e -iω 2) N｜F(e -iω )｜F(z) is a rational function), and then a class of symmetric wavelets including orthogonal B spline wavelets, and finally the best estimation of regular order obtained by analysing their regularity.

REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD

We consider the problem K（x）Uxx = utt , 0 〈 x 〈 1, t 〉 0, with the boundary condition u（O,t） = g（t） E LZ（R） and ux（O,t） = 0, where K（x） is continuous and 0 〈α≤ K （x） 〈 ＋∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u（x, .） E H2（R） and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem.

基于视觉传达技术的激光光斑图像超分辨率重建方法

激光光斑图像在成像过程中易受到成像条件和成像方式的限制,导致激光光斑图像的分辨率比较低,难以满足实际需求。为此,提出基于视觉传达技术的激光光斑图像超分辨率重建方法。采用视觉传达技术采集激光光斑图像,并使用双树复小波阈值方法对激光光斑图像去噪处理,通过改进稠密神经网络提取激光光斑图像特征,基于奇异值分解方法降低字典中原子的数目,改进稀疏表达正则化方法,实现激光光斑图像的超分辨率重建。实验结果表明,所提方法的低分辨率图像重建结果与原始图像更加接近,重建图像的结构相似度均在0.9以上,证明该方法的重建效果好、更适合实际应用。

基于超拉普拉斯正则化的冲击波超压层析重建

超压层析成像是利用传感器采集到的冲击波信号来反演测试区域的超压分布,是典型的不完全数据重建问题,为了提高求解精度,本文提出了一种基于高斯牛顿迭代联合超拉普拉斯正则化的冲击波超压层析重建方法。由于实际采集到的冲击波信号通常与干扰信号混叠在一起,会影响超压值的测量精度,本文首先采用改进的小波阈值算法对冲击波信号进行去噪处理;其次利用超拉普拉斯先验对图像边缘和二维层析模型进行正则约束;然后采用高斯牛顿迭代算法和交替方向乘子算法,解决大型病态稀疏矩阵的求解问题。实际实验结果表明本文的正则化方法与传统的全变分正则化和广义全变分正则化相比,重建精度可保持在15%左右,在实际场景中具有一定的应用价值。

Wavelet-based deconvolution of ultrasonic signals in nondestructive evaluation

In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in the nondestructive evaluation field, which is based on the theory of Fourier-Wavelet regularized deconvolution (ForWaRD). This new approach can be viewed as a solution to the open problem of adaptation of the ForWaRD framework to perform the convolution kernel estimation and deconvolution interdependently. The results indicate stable solutions of the esti- mated pulse and an improvement in the radio-frequency (RF) signal taking into account its signal-to-noise ratio (SNR) and axial resolution. Simulations and experiments showed that the proposed approach can provide robust and optimal estimates of the reflectivity function.

基于WPT-ISO-RELM模型的月径流时间序列预测研究

为提高月径流时间序列的预测精度,提升基本蛇群优化(SO)算法搜索能力,同时提升正则化极限学习机(RELM)预测性能,提出了小波包变换(WPT)-改进蛇群优化(ISO)算法-RELM预测模型。首先,利用WPT将月径流时间序列分解为低频分量和高频分量;其次,通过构建8个RELM超参数寻优适应度函数对ISO寻优能力进行检验,并与SO算法、灰狼优化(GWO)算法、变色龙群算法(CSA)、鲸鱼优化算法(WOA)、樽海鞘群体算法(SSA)、侏獴优化算法(DMO)、粒子群优化算法(PSO)的优化结果作对比;最后,建立WPT-ISO-RELM模型,并构建包含WPT-SO-RELM在内的17种模型作对比模型,通过黑河流域莺落峡水文站、讨赖河水文站2个月径流预测实例对各模型进行验证。结果表明:①ISO寻优精度优于SO、GWO、CSA、WOA、SSA、DMO、PSO,通过关键参数的改进,能有效提升ISO的极值寻优能力和平衡能力;②WPT-ISO-RELM模型对莺落峡水文站、讨赖河水文站月径流预测的平均绝对百分比误差分别为0.854%、0.447%,平均绝对误差分别为0.245、0.068 m^(3)/s,纳什效率系数均在0.9999以上,优于其他对比模型,具有更高的预测精度和更好的稳健性;③ISO对于高维和低维问题均具有较好的优化效果,算法寻优能力对提升RELM预测精度十分关键,算法优化性能越强,寻优精度越高,由此获得的RELM超参数越优,所构建的模型预测性能越好。

Wavelet packet-based identification of complex oscillation in biological signals

Owing to the intrinsic nonlinearities of the system,a contracting mechanism,such as myogenic response,may induce different oscillatory patterns.Many specialists discussed the relations of oscillatory patterns with intrinsic control system or some pathological condition,but there is no single,well-defined criterion to achieve the identification of regular,stochastic,and chaotic activities.In this paper,we focus on the Mallat algorithm of wavelet packet and use it in the identification of the regular periodic,stochastic,and chaotic fluctuations.According to the specific frequency configuration of the chaos activity,we select proper layers of decomposition of wavelet packet and did fine segments to the frequency of signals.The frequency band of energy convergence could be recognized.The signal of periodic,stochastic,and chaotic could be distinguished depending on it.Numerical experiment is given to show its efficiency.Experiments on 12 babies' lung data have been done.This identification by means of wavelet packet could support the cardiologist or cerebral specialist to do more observation and deeper analysis to physic signals.

Wavelets and Entropy for Power Quality Assessment

In this paper, wavelet transform and entropy are evaluated using the mathematical analysis concepts of reflexibility, regularity and series obtention, these concepts remark the reason to make a selective reference framework for power quality applications. With this idea the paper used the same treatment for the two algorithms (Multiresolution and Multiscale Entropy). The wavelet is denoted to have the most power full consistence to the light off the reflexibility, regularity and series obtention. The paper proposes a power quality technique namely MpqAT.

Performance Evaluation of Wavelet Based on Human Visual System

We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function (MTF) of human visual system in the frequency domain. In this paper, we evaluate performance of the constructed wavelet, and compare it with the widely used Daubechies 9 7, Daubechies 9 3 and GBCW 9 7 wavelets. The result shows that coding performance of the constructed wavelet is better than Daubechies 9 3, and is competitive with Daubechies 9 7 and GBCW 9 7 wavelets. Like Daubechies 9 3 wavelet, the filter coefficients of the constructed wavelet are all dyadic fractions, and the tap is less than Daubechies 9 7 and GBCW 9 7. It has an attractive feature in the realization of discrete wavelet transform.

A wavelet-based super-resolution method for multi-slice MRI

In multi-slice magnetic resonance imaging (MRI), the resolution in the slice direction is usually reduced to allow faster acquisition times and to reduce the amount of noise in each 2D slice. To address this issue, a number of super resolution (SR) methods have been proposed to improve the resolution of 3D MRI volumes. Most of the methods involve the use of prior models of the MRI data as regularization terms in an ill-conditioned inverse problem. The use of user-defined parameters produces better results for these approaches but an inappropriate choice may reduce the overall performance of the algorithm. In this paper, we present a wavelet domain SR method which uses a Gaussian scale mixture (GSM) model in a sparseness constraint to regularize the ill-posed SR inverse problem. The proposed approach also makes use of an extension of the Dual Tree Complex Wavelet Transform to provide the ability to analyze the wavelet coefficients with sub-level precision. Our results show that the 3D MRI volumes reconstructed using this approach have quality superior to volumes produced by the best previously proposed approaches.

Construction of nonseparable orthonormal compactly supported wavelet bases for L^2(R^d)

Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].

复杂背景下医学图像规则区域纹理缺陷识别

由于当前已有方法未能对医学图像进行去噪处理,导致纹理缺陷识别耗时较长,识别结果不准确。提出一种复杂背景下医学图像规则区域纹理缺陷识别方法,首先采用系数关联方法将医学图像小波分解后的高频分量作为噪声和边缘,假设小波系数被标记为边缘,则保持不变;反之,则采用邻域方法进行系数收缩;对经过处理的小波系数进行平稳小波逆变换,获取去噪后的医学图像。然后引入Retinex理论对医学图像的细节进行增强调整;同时通过Hough变换对复杂背景下的医学图像规则区域纹理缺陷进行特征提取,实现缺陷识别。最终进行实验测试,结果表明所提方法可以获取高效率、高精度的医学图像规则区域纹理缺陷识别结果。

三维空间VR成像的小区域目标跟踪仿真

对VR图像目标跟踪的是对图像下一帧可能状态的预测,为图像处理提供先验知识,以寻找当前帧图像中最优目标位置。但由于虚拟三维空间小区域图像目标特征覆盖率较大,小目标的跟踪难度较高,为此,提出基于背景约束与卷积特征的VR成像小区域目标跟踪方法。引入三维成像自旋模型,获取虚拟三维空间VR图像。采用中值滤波和小波系数变化算法消除图像中的噪声,避免跟踪过程受到噪声干扰。基于此,通过引入背景约束,通过设置记忆滤波器与卷积特征滤波器实现VR图像的小目标检测,完成虚拟三维空间VR成像小区域目标的跟踪。实验结果表明,研究方法的目标跟踪位置误差低于0.5mm,每秒钟可完成约16幅VR图像小区域目标的跟踪,且小目标跟踪成功率接近100%,所得到的VR图像可视化效果更好。

低幅度薄储层区块的目标处理及应用效果

P区块位于哈萨克斯坦的南图尔盖盆地,有利勘探目标侏罗纪地层属于陆相碎屑沉积。由于湖水进退频繁,造成砂体储层薄、横向变化快,且该区的构造圈闭幅度较小。针对该地区的地质和地球物理资料特点,通过开展目标处理技术的研究和应用以提高地震资料的品质。利用微测井约束的层析静校正提高低幅度构造的成像精度;通过井控子波处理提高地震数据的纵向分辨率,利用OVT域规则化改善观测系统的空间采样属性,提高资料的信噪比和横向分辨率;应用VSP速度、声波测井速度约束地震速度以改进地震速度分析的可靠性,满足低幅度薄储层成像对速度精度的要求。结果表明,目标处理技术的应用提高了研究区地震资料的成像精度和纵横向分辨率,满足低幅度薄储层的勘探要求,为落实该区块低幅度构造高产油藏提供了可靠的基础。

数字图像复原技术综述

数字图像复原的目的是将所观测到的退化图像恢复到退化前的原始图像,该恢复过程在很多图像处理应用中至关重要。近年来,图像复原技术虽已得到广泛研究,但仍有值得改进之处。为了使该领域的研究人员对当前各种图像复原方法有较全面的了解,在众多技术文献中选取了具有典型性的95篇来对各种图像复原方法进行分类综述。首先通过对复原技术问题的描述,揭示了复原技术的数学背景;其次以数字图像复原技术发展为主线,将复原方法归结为两大类进行详细讨论。一类是经典图像复原方法,另一类是现代图像复原方法。前者反应复原技术背景与发展过程,后者体现复原技术的发展趋势与面临的困难。最后,在总结全文的基础上,指出在今后进一步研究中值得关注的7项问题。

故障信号检测的小波基选择方法

提出了一种用于故障信号奇异性检测的小波基选择方法—按照小波规则性系数选择小波基。这一方法是基于小波变换后的小波系数表示小波函数和信号之间的相似程度,同时信号的规则性系数又和小波变换后的小波系数模值间存在着一定关系。仿真结果表明,这一方法的有效性和可行性。

去噪正则化模型修正方法在桥梁损伤识别中的应用

以传统基于灵敏度分析的有限元模型修正方法为基础,提出一种结合小波去噪过程的正则化模型修正损伤识别方法。为改进模型修正方法损伤识别效果,一方面利用有损结构模态与模态噪声的波形在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,并利用修正后的模态构造目标函数;一方面采用正则化方法改善反问题求解的非适定性。由于从输入数据和求解过程两方面同时改善了结构损伤识别反问题的求解,因此可以有效抑制实测模态参数中噪声的影响,正确识别结构损伤。以连续梁桥模型为例的损伤识别数值模拟表明,所提出方法在保持识别算法鲁棒性、抑制噪声的同时,可有效提高桥梁结构损伤的识别精度。

一种基于正则化方法的准最佳图像复原技术

提出一种基于正则化方法的高效图像复原技术.正则化残量的能量越小,则恢复效果越好,基于此,利用小波变换定性地分析如何选取正则化算子,利用随机理论得到正则化残量的能量期望值,通过最小化这个期望模型确定正则化参数,从而得到正则化图像.定性分析表明,在通常情况下应选取低阻高通的正则化算子.实验结果表明,该恢复技术比传统方法的恢复性能要好,恢复效果接近最佳且性能稳定.

小波构造变正则参数变分模型在带噪图像恢复中的应用

在利用正则化方法构造变分模型进行图像去噪时 ,其正则参数往往选择为恒定值 文中利用小波分解的层次性和带噪图像中噪声所具有的时频特点 ,构造出变正则参数的变分模型 在不同的小波分解层 。

一种基于小波变换的迭代正则化图象恢复算法

提出一种基于小波变换的迭代正则化图象恢复算法，兼顾抑制噪声的增长和保留图象重要边界。该算法根据图象小波变换各个子频段的不同频率特性和方向特性，分别采用不同的正则化参数和正则化算子。实验结果表明采用该算法的图象恢复的性能优于常规的空域算法。