WAVELET-BASED FAIRING OF B-SPLINE SURFACES

A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduced to approximate a B spline surface by a quasi uniform one. An error control approach for wavelet based fairing is suggested. Samples are given to show the feasibility of the algorithms presented in this paper. The practice showed that the wavelet based fairing is better than energy based one in case where the number of vertices of the B spline surface is greater than 1000. The quantitative variance of the approximation error in accordance with the change of decomposition levels needs to be further explored.

Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications

We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.

Characteristics and method of synthesis seismic wave based on wavelet reconstruction

A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it as criterion, the formula of synthesizing seismic wave is deduced. Using the design parameters specified in Chinese Seismic Design Code for buildings, seismic waves are synthesized. Moreover, the method of selecting wavelet bases in synthesizing seismic wave and the influence of the damping ratio on synthesizing results are analyzed. The results show that the synthesis seismic waves using wavelet bases can represent the characteristics of the seismic wave as well as the ground characteristic period, and have good time-frequency non-stationary.

The Boundary Processing of Wavelet Based Image Compression

When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.

CONSTRUCTION METHODS AND ALGORITHM DESIGN OF WAVELET BASES

Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper.

Detection of Edge with the Aid of Mollification Based on Wavelets

In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.

Practical Non-Uniform Channelization for Multistandard Base Stations

A multistandard software-defined radio base station must perform non-uniform channelization of multiplexed frequency bands. Non-uniform channelization accounts for a significant portion of the digital signal processing workload in the base station receiver and can be difficult to realize in a physical implementation. In non-uniform channelization methods based on generalized DFT filter banks, large prototype filter orders are a significant issue for implementation. In this paper, a multistage filter design is applied to two different non-uniform generalized DFT-based channelizers in order to reduce their filter orders. To evaluate the approach, a TETRA and TEDS base station is used. Experimental results show that the new multistage design reduces both the number of coefficients and operations and leads to a more feasible design and practical physical implementation.

A NEW ADAPTIVE FILTERING SCHEME BASED ON WAVELET TRANSFORM

Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.

WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA

This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

WAVELET-BASED FINE GRANULARITY SCALABLE VIDEO CODING

This letter proposes an efficient wavelet-based Fine Granularity Scalable (FGS)coding scheme, where the base layer is encoded with a newly designed wavelet-based coder, and the enhancement layer is encoded with Progressive Fine Granularity Scalable (PFGS) coding.This algorithm involves multi-frame motion compensation, rate-distortion optimizing strategy with Lagrangian cost function and context-based adaptive arithmetic coding. In order to improve efficiency of the enhancement layer coding, an improved motion estimation scheme that uses both information from the base layer and the enhancement layer is also proposed in this letter. The wavelet-based coder significantly improves the coding efficiency of the base layer compared with MPEG-4 ASP (Advanced Simple Profile) and H.26L TML9. The PFGS coding is a significant improvement over MPEG-4 FGS coding at the enhancement layer. Experiments show that single layer coding efficiency gain of the proposed scheme is about 2.0-3.0dB and 0.3-1.0dB higher than that of MPEG-4 ASP and H.26L TML9, respectively. The overall coding efficiency gain of the proposed scheme is about 4.0-5.0dB higher than that of MPEG-4 FGS.

Performance Analysis of an Optimal Circular 16-QAM for Wavelet Based OFDM Systems

The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.

Theory and Application of Natural-Based Wavelet Method

Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.

Correlation methods of base-level cycle based on wavelet neural network

The authors discussed the method of wavelet neural network(WNN) for correlation of base-level cycle.A new vectored method of well log data was proposed.Through the training with the known data set,the WNN can remenber the cycle pattern characteristic of the well log curves.By the trained WNN to identify the cycle pattern in the vectored log data,the ocrrelation process among the well cycles was completed.The application indicates that it is highly efficient and reliable in base-level cycle correlation.

面向多浓度非均匀云雾的双域遥感图像去雾算法

光学遥感卫星图像容易受到多浓度非均匀云雾的干扰,造成图像质量严重退化。现有的去雾算法难以有效处理多浓度非均匀云雾,于是提出了一种自注意力强化机制,即在自注意力变换中引入一种简单的无参注意力(SimAM)增强自注意力变换的建模能力,提高对非均匀云雾的感知;为进一步提高网络的纹理细节表征能力,设计了新颖的差分卷积细节增强块,利用差分卷积算子引入梯度级信息,提高去雾网络对纹理细节的恢复能力;为实现RGB域和自适应小波域联合去雾,引入深度自适应提升小波变换实现自适应小波空间,从而实现双域协同去雾。实验结果表明,提出的方法在主流的遥感图像去雾数据集上相较于骨干模型,获得了0.52 dB的PSNR总增益。

基于Mask R-CNN的电力关键设备载波运行状态检测

为解决因载波信号大幅波动造成的电力设备运行状态检测失准问题,提出基于Mask R-CNN的电力关键设备载波运行状态检测方法。在Mask R-CNN网络模型中,通过定义小波基向量的方法确定电力载波暂态系数的计算结果。联合电量阻抗特征,求解连续阈值区间表达式,将获取到的电力载波信号放置在已定义阈值区间内。计算奇异值检测系数的取值条件,完成电力关键设备载波运行状态检测。对比实验结果表明,所提方法可以将电力载波信号波动幅值控制在±17 dB之间,对载波信号波动行为起到了明显的抑制作用,能够提升电网主机对电力设备运行状态检测的准确性。

基于小波基特征提取的苹果叶部病害检测算法设计

针对苹果叶部常见病害实现绿色、无损检测,提出了一种基于SVM和小波基特征提取的苹果叶部病害识别算法。该算法通过对苹果叶片图像进行小波变换,提取出小波系数后,进一步执行小波包变换,再提取出具有代表性的小波基特征,根据每个区域的特征参数,得到一组小波基特征向量,然后通过SVM进行模型训练,使用SVM分类器对不同病害进行分类识别。试验结果表明,基于小波基特征提取的苹果叶部病害识别算法,识别常见五种苹果叶部病害准确率较高,可靠性较好,满足实际生产中对苹果叶部病害无损检测的需求,为绿色、智慧果业提供技术支持。

基于优化分解与误差修正的光伏发电功率预测

针对光伏发电功率预测精度不高的问题,提出一种基于优化分解降噪联合误差修正模型。该模型分为3个阶段,第一阶段,首先用基于全局搜索的鲸鱼优化算法(GSWOA)选取变分模态分解(VMD)的参数,之后运用优化后的VMD对原始数据进行分解;然后利用互相关分析重构高频分量,最后对高频分量进行小波软阈值降噪(WTSD);第二阶段,运用门控循环单元(GRU)对每个分量进行预测,将所有分量预测结果叠加起来得到初步预测结果;第三阶段,对初始预测结果进行误差修正(EC)。为验证模型的有效性,利用宁夏太阳山光伏电站2021年1、4、7、10月份的光伏实测数据进行实验,实验结果表明,相比于LSTM、GRU、VMD-LSTM,该混合模型表现出更好的性能。

FAULT DIAGNOSIS APPROACH FOR ROLLER BEARINGS BASED ON EMPIRICAL MODE DECOMPOSITION METHOD AND HILBERT TRANSFORM

Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.

Wavelet-Galerkin方法在微分方程中的应用

运用小波理论,针对某一类变系数微分方程,首次将Littlewood-paley小波引入到变系数微分方程求解中,得到了Littlewood-paky小波ψ的尺度函数(?),构造了L2[0,1]中的正交小波基ψj,kfold,证明了该正交小波基满足方程的初始条件.运用Galerkin方法求出了方程在子空间中的逼近解,得出了变系数微分方程的准确解.拓宽了小波理论的适用范围,并为微分方程的求解问题提供了新的理论空间.

ORTHONORMAL POLYNOMIAL BASSES AND WAVELET-PACKETS

For any fixed ε > 0, an explicit construction of anorthonormal trigonometric polynomial basis {Tk}∞k=1 inL2 [0,1) with degTk≤ 0.5(1 +ε)k is presented. Thus weimprove the results obtained by D. Offin and K. Oskolkov in [4] and by Al. A. Privalov in [6]. and practically solve the open problemasked in [4], [8] and [9]. Moreover, as in [4], Fourier sums with respectto this polynomial basis are projectors onto subspaces of trigonometricpolynomials of high degree, which implies almost best approximation- properties.