Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

Multiresolution Terrian Model in GIS

DEM, which becomes a major component of geographic information processing in earth and engineering sciences, has been studied in the GIS literature for a long time. We use DEM to represent the terrain in GIS. The more data are available, the better representations of a terrain can be built. But not all tasks in the framework of a given application necessarily require the same accuracy, and even a single task may need different levels of accuracy in different areas of the domain. Multiresolution models, such as LOD, offer the possibility of representing and analyzing a terrain at a range of different levels of detail. In this paper, some key issues in multiresolution DEM model are studied. Three main models are focused on Hierarchical TIN(HTIN), multiresolution terrain model based Delaunay and Hierarchical Dynamic Simplification. The advantages and disadvantages of these methods are analyzed. The technology of tile to tile edge match is studied to maintain the consistency between adjacent edges and tile edges in HTIN model. And the Hypergraph based Objected oriented Model(HOOM) is presented to divide and code spatial area and describe the terrain feature in adding and deleting points based on Delaunay rule retriangulating. The conclusions have been drawn in the end.

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 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.

An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations

This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equa-tions.The solutions to such equations often exhibit solitary wave and local structures,which make adaptivity essential in improving the simulation efficiency.Our scheme uses the ultra-weak discontinuous Galerkin(DG)formulation and belongs to the framework of adaptive multiresolution schemes.Various numerical experiments are presented to demon-strate the excellent capability of capturing the soliton waves and the blow-up phenomenon.

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.

MULTIRESOLUTION SYMPLECTIC SCHEME FOR WAVE PROPAGATION IN COMPLEX MEDIA

A fast adaptive symplectic algorithm named Multiresolution Symplectic Scheme (MSS) was first presented to solve the problem of the wave propagation (WP) in complex media, using the symplectic scheme and Daubechies' compactly supported orthogonal wavelet transform to respectively discretise the time and space dimension of wave equation. The problem was solved in multiresolution symplectic geometry space under the conservative Hamiltonian system rather than the traditional Lagrange system. Due to the fascinating properties of the wavelets and symplectic scheme, MSS is a promising method because of little computational burden, robustness and reality of long-time simulation.

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.

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.

A Multiresolution Reconstructive Algorithm Based on Network Theory for Electrical Capacitance Tomography

Electrical capacitance tomography technique reconstructs dielectric constant distribution in an object by measuring the capacitances between the eletrode pairs which are mounted around this object. Because of the limitation of measurement condition, the measured data are imcomplet. This paper describes a multiresolution reconstructive algorithm which is based on network theory for electrical capacitance tomography technique. The dielectric constant distribution of flow of two components in a pipeline is reconstructed. The algorithm is as follows: Firstly, construct a rough, first level system model, and assume the dielectric constant distribution of the region to be reconstructed. After iteration, the dielectic constant of each unit can be reconstructed. Secondly, construct a finer, second level the system model and determine the initial dielectric constant of each unit in the region to be reconstructed according to related information between two levels. After iteration, the image of the pipeline's cross section can be reconstructed. The results of simulated experiments about different kinds of medium distributions show that this algorithm is effective and can converge.

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.

A novel vague set approach for selective contrast enhancement of mammograms using multiresolution

The proposed algorithm introduces a novel vague set approach to develop a selective but robust, flexible and intelligent contrast enhancement technique for mammograms. Wavelet based filtering analysis can produce Low Frequency (LF) and High Frequency (HF) subbands of the original input images. The extremely small size microcalcifications become visible under multiresolution techniques. LF subband is then fuzzified by conventional fuzzy c-means clustering (FCM) algorithm with justified number of clusters. HF components, representing the narrow protrusions and other fine details are also fuzzified by FCM with justified number of clusters. Vague set approach captures the hesitancies and uncertainties of truly affected masses/other breast abnormalities with normal glandular tissues. After highlighting the masses/microcalcifications accurately, both LF and HF subbands are transformed back to the original resolution by inverse wavelet transform. The results show that the proposed method can successfully enhance the selected regions of mammograms and provide better contrast images for visual interpretation.

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.

The Multiresolution Image Format

In this paper we present a new method and file format which allows to create, store and manipulate multiresolution raster images. “Classic” raster images are built up by rasters (pixels) where in the same image each raster (pixel) has the same size. Multiresolution raster image (mri) are unlike the “classic” raster images. An mri file is a regular text file, conformed xml 1.0 standard and allows: 1) to store raster based images with different resolution in the same file and in the same time (i.e., allows to contain rasters with different size in the same image);2) to export easily any part of the image as a separate raster image and to import an image as a part of a raster;3) to define geographical reference for a raster image and use this image as a raster based GIS model;4) to perform computations (i.e., image manipulation) on the content of the file. It is an important characteristic of the mri format that mathematical operations could be performed always in the same resolution as the current resolution of the given part of the image. To confirm this statement we present how to perform a convolution on an mri file.

A Multiresolution Channel Decomposition for H.264/AVC Unequal Error Protection

The most commonly used transmission channel in nowadays provides the same level of protection for all the information symbols. As the level of protection should be adequate to the importance of the information set, it is justified to use UEP channels in order to protect information of variable importance. Multiresolution channel decomposition has emerged as a strong concept and when combined with H.264/AVC layered multiresolution source it leads to outstanding results especially for mobile TV applications. Our approach is a double multiresolution scheme with embedded constellation modulations on its baseband channels followed by OFDM time/frequency multiresolution passband modulation. The aim is to protect The NAL units carrying the most valuable information by the coarse constellations into coarse sub-channels, and the NAL units that contain residual data by fined constellations and transposed into the fined OFDM sub-channels. In the multiresolution protection coding, our approach is a multiresolution decomposition of the core convolutional constituent of the PCCC where the NAL units carrying the most valuable information are coded by the rugged coefficient of the multiresolution code and the NAL units that contains residual data are coded by refined less secure coding coefficients.

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.

Multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

This study proposes a B-spline-based multiresolution and multimaterial topology optimization(TO)design method for fail-safe structures(FSSs),aiming to achieve efficient and lightweight structural design while ensuring safety and facilitating the postprocessing of topological structures.The approach involves constructing a multimaterial interpolation model based on an ordered solid isotropic material with penalization(ordered-SIMP)that incorporates failsafe considerations.To reduce the computational burden of finite element analysis,we adopt a much coarser analysis mesh and finer density mesh to discretize the design domain,in which the density field is described by the B-spline function.The B-spline can efficiently and accurately convert optimized FSSs into computer-aided design models.The 2D and 3D numerical examples demonstrate the significantly enhanced computational efficiency of the proposed method compared with the traditional SIMP approach,and the multimaterial TO provides a superior structural design scheme for FSSs.Furthermore,the postprocessing procedures are significantly streamlined.

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.

Multiresolution analysis of density fluctuation in supersonic mixing layer

Due to the difficulties in measuring supersonic density field, the multiresolution analysis of supersonic mixing layer based on experimental images is still a formidable challenge. By utilizing the recently developed nanoparticle based planar laser scattering method, the density field of a supersonic mixing layer was measured at high spatiotemporal resolution. According to the dynamic behavior of coherent structures, the multiresolution characteristics of density fluctuation signals and density field images were studied based on Taylor’s hypothesis of space-time conversion and wavelet analysis. The wavelet coefficients reflect the characteristics of density fluctuation signals at different scales, and the detailed coefficients reflect the differences of approximation at adjacent levels. The density fluctuation signals of supersonic mixing layer differ from the periodic sine signal and exhibit similarity to the fractal Koch signal. The similarity at different scales reveals the fractal characteristic of mixing layer flowfield. The two-dimensional wavelet decomposition and reconstruction of density field images extract the approximate and detailed signals at different scales, which effectively resolve the characteristic structures of the flowfield at different scales.