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.

The Biorthogonality of Multiple Vector-valued Bivariate Wavelet Packets

The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.

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.

Vector-intensity measure based seismic vulnerability analysis of bridge structures

This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure （viM）, which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa（T1） and Sa（T2） are chosen as viM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on viM is studied with Duunett- Sobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to viM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.

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.

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 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.

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.

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

珍视向量的 multiresolution 分析的观点被介绍，有3规模的直角的珍视向量的小浪的概念是直角的珍视向量的小浪的存在上的状况借助于 paraunitary 向量过滤器银行 theory.An 算法被给的必要、足够的 proposed.A 因为构造简洁地支持的直角的珍视向量的小浪的一个班是 presented.Their 特征被讨论由操作员理论的优点，时间频率 method.Moreover ，它被看

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 particle swarm optimization (PSO) and wavelet analysis is proposed for achieving higher identification precision.Input-output data of hydraulic flight simulator were decomposed by wavelet multiresolution 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.