MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Study on spillover effect of copper futures between LME and SHFE using wavelet multiresolution analysis

Research on information spillover effects between financial markets remains active in the economic community. A Granger-type model has recently been used to investigate the spillover between London Metal Exchange(LME) and Shanghai Futures Exchange(SHFE) ,however,possible correlation between the future price and return on different time scales have been ignored. In this paper,wavelet multiresolution decomposition is used to investigate the spillover effects of copper future returns between the two markets. The daily return time series are decomposed on 2n(n=1,…,6) frequency bands through wavelet mul-tiresolution analysis. The correlation between the two markets is studied with decomposed data. It is shown that high frequency detail components represent much more energy than low-frequency smooth components. The relation between copper future daily returns in LME and that in SHFE are different on different time scales. The fluctuations of the copper future daily returns in LME have large effect on that in SHFE in 32-day scale,but small effect in high frequency scales. It also has evidence that strong effects exist between LME and SHFE for monthly responses of the copper futures but not for daily responses.

FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS

We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.

HOUSE EXTRACTION WITH MULTIRESOLUTION ANALYSIS AND INFORMATION FUSION

Houses are key elements both in aerial photographs and maps.Their extraction has significance not only to military,but also to automatical rela-tive orientation,automatical absolute orientation,feature-based matching,sys-tematic description,automatic data aquisition,structure analysis,image under-standing,digital mapping,and construction of urban geographic information sys-tem（UGIS）.For this purpose,this paper mainly addresses:（1）a brief introduc-tion to the multiresolution analysis of wavelet theory and its difference formLaplacian pyramid,（2）how to generate the multiresolution images and edge fea-tures,and（3）how to employ these multiresolution images and edge features toextract the houses from aerial photographs by multiresolution structure and infor-mation fusion.

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes(SNN) and local-Delaunay-triangulation(LDT) tech-niques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h-adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h-adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

Scale-Dependent Representations of Relief Based on Wavelet Analysis

Automatic generalization of geographic information is the core of multi_scale representation of spatial data,but the scale_dependent generalization methods are far from abundant because of its extreme complicacy.This paper puts forward a new consistency model about scale_dependent representations of relief based on wavelet analysis,and discusses the thresholds in the model so as to acquire the continual representations of relief with different details between scales.The model not only meets the need of automatic generalization but also is scale-dependent completely.Some practical examples are given.

Multiresolution Isogeometric Topology Optimisation Using Moving Morphable Voids

A general and new explicit isogeometric topology optimisation approach with moving morphable voids(MMV)is proposed.In this approach,a novel multiresolution scheme with two distinct discretisation levels is developed to obtain high-resolution designs with a relatively low computational cost.Ersatz material model based on Greville abscissae collocation scheme is utilised to represent both the Young’s modulus of the material and the density field.Two benchmark examples are tested to illustrate the effectiveness of the proposed method.Numerical results show that high-resolution designs can be obtained with relatively low computational cost,and the optimisation can be significantly improved without introducing additional DOFs.

Multiresolution Finite Element Method Based on a New Locking-Free Rectangular Mindlin Plate Element

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.

ADAPTIVE MULTIRESOLUTION SPEECH ENHANCEMENT ALGORITHM BASED ON WAVELET TRANSFORM

In this paper, an adaptive multiresolution speech enhancement algorithm based on wavelet transform is put forward. It can make adaptive filtering to noise speech both at scales and among scales. So that the noise parts during the frequency intervals which decrease hearing quality mostly are reduced efficiently. Both the SNR and subject hearing quality of denoised speech are high and good.

SUPPRESSING THE COHERENT SPECKLE OF SAR IMAGES WITH WAVELET ANALYSIS

This paper studies Synthetic Aperture Radar (SAR) images contaminated by the coherent speckle noise with the multiresolution analysis of wavelet transform. This study shows that the influences of the speckle on different frequency components of the SAR image are different, and that the SAR image and the speckle have different manners of singularity. So, this paper presents a denoising method of wavelet analysis to reduce the speckle. Some experiments approve that this method not only suppresses the speckle effectively, but also preserves as much target characteristics of the original image as possible. It shows that this denoising method of wavelet analysis offers a very attractive alternative to suppress the coherent speckle noise of the SAR image.

Application of wavelet analysis to fault diagnosis of angular measuring system

For fault diagnosis, signal singularity and irregularity discontinuity fraction are very significant characteristics of signal. The discontinuity of output signal represents a system fault . In an angular measuring system, function transformer uses two D/A convertors, output circuit fault of a D/A convertor brings about discontinuity of one phase input voltage amplitude of inductosyn, results in a system error exceeding the allowable error and reduces the system accuracy. This is the reason why discontinuity is detected. Fourier transform has no resolution ability in angular domain, but wavelet can analyse signal in angular and frequency domains. So we decompose the error signal of angular measuring system by wavelet, detect the signal singularity at high frequency layer and find out the accurate position of it.

Multiresolutional Maneuvering Target Tracking Fusion Algorithm Based on Singular Sensor and Multipale Models

Multiresolutional signal processing has been employed in image processing and computer vision to achieve improved performance that cannot be achieved using conventional signal processing techniques at only one resolution level [1,2,5,6] . In this paper,we have associated the thought of multiresolutional analysis with traditional Kalman filtering and proposed A new fusion algorithm based on singular Sensor and Multipale Models for maneuvering target tracking.

Model identification of hydraulic flight simulator based on improved particle swarm optimization and wavelet analysis

A new model identification method of hydraulic flight simulator adopting improved panicle swarm optimization （PSO） and wavelet analysis is proposed for achieving higher identification precision. Input-output data of hydraulic flight simulator were decomposed by wavelet muhiresolution to get the information of different frequency bands. The reconstructed input-output data were used to build the model of hydraulic flight simulator with improved particle swarm optimization with mutation （IPSOM） to avoid the premature convergence of traditional optimization techniques effectively. Simulation results show that the proposed method is more precise than traditional system identification methods in operating frequency bands because of the consideration of design index of control system for identification.

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.

Multiresolution for Closed Curves and Surfaces Using Wavelets

Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.

星载材料极弱剩磁测量方法研究

为解决科学探测卫星星载材料微弱磁性测量难题,本文提出了一种卫星部件极弱剩磁的测量方法,并研制了测量系统。利用屏蔽技术去除外界磁场干扰,在屏蔽系统内搭建了测量系统,使用零场原子磁力仪采集旋转试件的磁场频谱信息,通过小波多分辨分析方法处理得到试件的磁特征数据。研究表明:本文方法可有效提取极弱剩磁信号,且系统稳定度优于1×10^(-12) T/30 min,磁场分辨率优于1×10^(-12) T,磁矩提取分辨量级可达10^(-6) A·m^(2),为整星磁洁净控制和空间磁场高精度探测提供了途径。

小波数值方法及其在计算力学中的应用

随着力学研究不断向多学科交叉、跨尺度关联及极端环境影响推进,强非线性、强间断、多场强耦合、多尺度与复杂几何构型已成为解决各类力学问题定量分析所面临的共性特征.长期的定量研究表明,实现具有这类特征力学问题有效求解的核心之一,是构建在多尺度情形、非线性因素作用下具有准确识别、定位、捕获以及分离各个尺度特征尤其是小尺度局部特征能力的数值工具,这些能力包括大尺度低阶近似解与小尺度高阶微小截断误差的有效分离解耦.而小波理论固有的多分辨分析和时频局部化特性,以及丰富的基函数可选择性,恰好能满足这一数学特征需求,因此,可为发展各类复杂力学问题的高效定量求解方法提供有效的理论支撑和丰富多样的技术途径.基于这一事实,本文对小波理论进行了全面探讨,着重介绍了双正交多分辨分析的理论框架和常用小波基的构造方法.在此基础上,深入研究了有限区域上小波逼近格式的构建方法,并系统阐述了各类基于小波理论的数值方法的基本原理、发展历程及其优缺点.特别关注了近期出现的具有突出性能的几类新型小波方法,并详细评述了它们在典型力学问题求解中的应用效果.同时,本文也指出了当前小波方法在复杂强非线性力学问题求解中所面临的挑战,旨在为小波数值方法的未来发展及其在复杂力学与工程问题中的应用拓展提供有益的参考,并为最终实现这些问题的高效、高精度普适定量求解提供新的视角和方法.

Multimodality Medical Image Fusion Based on Pixel Significance with Edge-Preserving Processing for Clinical Applications

Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many diseases.However,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing costs.To solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion performance.First,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing edges.The outputs of CBF are then subtracted from the original images to obtain detailed images.It further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural properties.These regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate size.The outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the edges.In addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical details.Numerous standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion results.Experimental results from the proposed research article exhibit superior performance compared to other competing techniques in the case of both qualitative and quantitative evaluation.In addition,the proposed method advocates less computational complexity and execution time while improving diagnostic computing accuracy.Nevertheless,due to the lower complexity of the fusion algorithm,the efficiency of fusion methods is high in practical applications.The results reveal that the proposed method exceeds the latest state-of-the-art methods in terms of providing detailed information,edge contour,and overall contrast.