Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Recognition of Hybrid PQ Disturbances Based on Multi-Resolution S-Transform and Decision Tree

Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on multiresolution S-transform and decision tree was proposed.Firstly,according to IEEE standard,the signal models of seven single power quality disturbances and 17 combined power quality disturbances are given,and the disturbance waveform samples are generated in batches.Then,in order to improve the recognition accuracy,the adjustment factor is introduced to obtain the controllable time-frequency resolution through multi-resolution S-transform time-frequency domain analysis.On this basis,five disturbance time-frequency domain features are extracted,which quantitatively reflect the characteristics of the analyzed power quality disturbance signal,which is less than the traditional method based on S-transform.Finally,three classifiers such as K-nearest neighbor,support vector machine and decision tree algorithm are used to effectively complete the identification of power quality composite disturbances.Simulation results showthat the classification accuracy of decision tree algorithmis higher than that of K-nearest neighbor and support vector machine.Finally,the proposed method is compared with other commonly used recognition algorithms.Experimental results show that the proposedmethod is effective in terms of detection accuracy,especially for combined PQ interference.

Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations

High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional problems.In our previous work(Lu et al.in Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse grids.In this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO scheme.Numerical experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids.

基于LOD四叉树算法的中尺度云团三维流场可视化模拟分析

中尺度环流在复杂的天气环境下时常被大尺度环流掩盖,不能及时获取中尺度云团的时空密度,影响了中尺度云团三维流场可视化模拟效果,为了提升可视化模拟性能,提出基于四叉树算法(levels of detail,LOD)的中尺度云团三维流场可视化模拟分析方法。分析了中尺度云团三维相对流场,从中获取了中尺度云团三维流场运动规律,并基于二维直方图取得中尺度云团三维流场特征;将粒子源与四叉树结构相结合,构成四叉树粒子系统,把取得的特征映射到系统内,利用该系统中的粒子完成中尺度云团三维流场的渲染绘制,从而实现中尺度云团三维流场的可视化模拟。实验结果表明,绘制帧率对比测试、可视化模拟速率对比测试和可视化模拟效果对比测试结果清晰度较高,可视化程度较高,实用性强、可靠性高。

Multi-resolution image segmentation based on Gaussian mixture model

Mixture model based image segmentation method, which assumes that image pixels are independent and do not consider the position relationship between pixels, is not robust to noise and usually leads to misclassification. A new segmentation method, called multi-resolution Ganssian mixture model method, is proposed. First, an image pyramid is constructed and son-father link relationship is built between each level of pyramid. Then the mixture model segmentation method is applied to the top level. The segmentation result on the top level is passed top-down to the bottom level according to the son-father link relationship between levels. The proposed method considers not only local but also global information of image, it overcomes the effect of noise and can obtain better segmentation result. Experimental result demonstrates its effectiveness.

Winter wheat identification by integrating spectral and temporal information derived from multi-resolution remote sensing data

Timely crop acreage and distribution information are the basic data which drive many agriculture related applications.For identifying crop types based on remote sensing,methods using only a single image type have significant limitations.Current research that integrates fine and coarser spatial resolution images,using techniques such as unmixing methods,regression models,and others,usually results in coarse resolution abundance without sufficient detail within pixels,and limited attention has been paid to the spatial relationship between the pixels from these two kinds of images.Here we propose a new solution to identify winter wheat by integrating spectral and temporal information derived from multi-resolution remote sensing data and determine the spatial distribution of sub-pixels within the coarse resolution pixels.Firstly,the membership of pixels which belong to winter wheat is calculated using a 25-m resolution resampled Landsat Thematic Mapper(TM)image based on the Bayesian equation.Then,the winter wheat abundance(acreage fraction in a pixel)is assessed by using a multiple regression model based on the unique temporal change features from moderate resolution imaging spectroradiometer(MODIS)time series data.Finally,winter wheat is identified by the proposed Abundance-Membership(AM)model based on the spatial relationship between the two types of pixels.Specifically,winter wheat is identified by comparing the spatially corresponding 10×10 membership pixels of each abundance pixel.In other words,this method takes advantage of the relative size of membership in a local space,rather than the absolute size in the entire study area.This method is tested in the major agricultural area of Yiluo Basin,China,and the results show that acreage accuracy(Aa)is 93.01%and sampling accuracy(As)is 91.40%.Confusion matrix shows that overall accuracy(OA)is 91.4%and the kappa coefficient(Kappa)is 0.755.These values are significantly improved compared to the traditional Maximum Likelihood classification(MLC)and Random Forest classification(RFC)which rely on spectral features.The results demonstrate that the identification accuracy can be improved by integrating spectral and temporal information.Since the identification of winter wheat is performed in the space corresponding to each MODIS pixel,the influence of differences of environmental conditions is greatly reduced.This advantage allows the proposed method to be effectively applied in other places.

Application of multi-resolution analysis in sonar image denoising

Sonar images have complex background, low contrast, and deteriorative edges; these characteristics make it difficult for researchers to dispose the sonar objects. The multi-resolution analysis represents the signals in different scales efficiently, which is widely used in image processing. Wavelets are successful in disposing point discontinuities in one dimension, but not in two dimensions. The finite Ridgelet transform （FRIT） deals efficiently with the singularity in high dimension. It presents three improved denoising approaches, which are based on FRIT and used in the sonar image disposal technique. By experiment and comparison with traditional methods, these approaches not only suppress the artifacts, but also obtain good effect in edge keeping and SNR of the sonar image denoising.

Multi-resolution EMD and classscatter matrix extracting of tank sound

The acoustic vibration signal of tank is disassembled into the sum of intrinsic mode function （IMF） by multi-resolution empirical mode decomposition （EMD） method. The instantaneous frequency is obtained, and feature transformation matrix is figured out by class scatter matrix. Multi- dimensional scale energy vector is mapped into low-dimensional eigenvector, and classification extraction is realized. This method sufficiently separates of different sound target features. The test result indicates that it is effective.

Magnetic-resonance image segmentation based on improved variable weight multi-resolution Markov random field in undecimated complex wavelet domain

To solve the problem that the magnetic resonance(MR)image has weak boundaries,large amount of information,and low signal-to-noise ratio,we propose an image segmentation method based on the multi-resolution Markov random field(MRMRF)model.The algorithm uses undecimated dual-tree complex wavelet transformation to transform the image into multiple scales.The transformed low-frequency scale histogram is used to improve the initial clustering center of the K-means algorithm,and then other cluster centers are selected according to the maximum distance rule to obtain the coarse-scale segmentation.The results are then segmented by the improved MRMRF model.In order to solve the problem of fuzzy edge segmentation caused by the gray level inhomogeneity of MR image segmentation under the MRMRF model,it is proposed to introduce variable weight parameters in the segmentation process of each scale.Furthermore,the final segmentation results are optimized.We name this algorithm the variable-weight multi-resolution Markov random field(VWMRMRF).The simulation and clinical MR image segmentation verification show that the VWMRMRF algorithm has high segmentation accuracy and robustness,and can accurately and stably achieve low signal-to-noise ratio,weak boundary MR image segmentation.

Convergence to Steady-State Solutions of the New Type of High-Order Multi-resolution WENO Schemes: a Numerical Study

A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the classical WENO schemes(Jiang and Shu in J Comput Phys,126:202-228,1996)might suffer from slight post-shock oscillations(which are responsible for the residue to hang at a truncation error level),this new type of high-order finite-difference and finite-volume multi-resolution WENO schemes is applied to control the slight post-shock oscillations and push the residue to settle down to machine zero in steady-state simulations.This new type of multi-resolution WENO schemes uses the same large stencils as that of the same order classical WENO schemes,could obtain fifth-order,seventh-order,and ninth-order in smooth regions,and could gradually degrade to first-order so as to suppress spurious oscillations near strong discontinuities.The linear weights of such new multi-resolution WENO schemes can be any positive numbers on the condition that their sum is one.This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finitedifference and finite-volume WENO schemes for solving steady-state problems.In comparison with the classical fifth-order finite-difference and finite-volume WENO schemes,the residue of these new high-order multi-resolution WENO schemes can converge to a tiny number close to machine zero for some benchmark steady-state problems.

Conformal Multi-resolution Time-Domain Method for Scattering Curved Dielectric Objects

A conformal multi-resolution time-domain( CMRTD) method is presented for modeling curved objects. The effective dielectric constant and area weighting are used to derive the update equations of CMRTD. The backward scattering bistatic radar cross sections( RCS) of the dielectric cylinder and ellipsoid are used to validate the proposed method. The results show that the proposed conformal method is more accurate to deal with the complex curved objects in electromagnetic simulations.

Fast image super-resolution algorithm based on multi-resolution dictionary learning and sparse representation

Sparse representation has attracted extensive attention and performed well on image super-resolution（SR） in the last decade. However, many current image SR methods face the contradiction of detail recovery and artifact suppression. We propose a multi-resolution dictionary learning（MRDL） model to solve this contradiction, and give a fast single image SR method based on the MRDL model. To obtain the MRDL model, we first extract multi-scale patches by using our proposed adaptive patch partition method（APPM）. The APPM divides images into patches of different sizes according to their detail richness. Then, the multiresolution dictionary pairs, which contain structural primitives of various resolutions, can be trained from these multi-scale patches.Owing to the MRDL strategy, our SR algorithm not only recovers details well, with less jag and noise, but also significantly improves the computational efficiency. Experimental results validate that our algorithm performs better than other SR methods in evaluation metrics and visual perception.

Runge-Kutta Multi-resolution Time-Domain Method for Modeling 3D Dielectric Curved Objects

A conformal Runge-Kutta multi-resolution time-domain(C-RKMRTD)method is present and applied to model and analyze curved objects.Compared with the non-conformal method,the proposed method is more accurate.The scattering analyses of the cylinder and ellipsoid are presented to validate the proposed method.The numerical results demonstrate that the proposed scheme perform better than the MRTD method and other higher order methods with a higher accuracy.

An image registration method based on multi-resolution morphology contour detection

Combined with the printing application,an image registration method based on the multi-resolution morphology contour detection was proposed.First,a direction based multi-resolution gray morphology in the scheme was proposed to realize the contour extraction.Then,based on the contour features,the subspace image registration was proposed to deal with issues of the computing complexity appeared in the traditional image registration methods.The proposed image registration was efficiently applied in the defect inspection of printing images.

Real-Time Rendering of Dynamic Clouds Using Multi-Resolution Adaptive Grids

The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between objects and clouds.Oriented bounding box(OBB)hierarchical trees of objects are established,and the resolutions of global and local grids can be selected automatically.The motion equations of fluid dynamics are simplified.Upwind difference is applied to ensure the stability of the simulation process during the discrete process of partial differential equations.To solve the speed problem of existed phase functions,the improved phase function is applied to the illumination calculation of clouds.Experimental results show that the proposed methods can promote the simulation efficiency and meet the need for the simulation of large-scale clouds scene.Real-time rendering of clouds and the interaction between clouds and objects have been realized without preprocessing stage.

Speech Intelligibility Enhancement Algorithm Based on Multi-Resolution Power-Normalized Cepstral Coefficients(MRPNCC)for Digital Hearing Aids

Speech intelligibility enhancement in noisy environments is still one of the major challenges for hearing impaired in everyday life.Recently,Machine-learning based approaches to speech enhancement have shown great promise for improving speech intelligibility.Two key issues of these approaches are acoustic features extracted from noisy signals and classifiers used for supervised learning.In this paper,features are focused.Multi-resolution power-normalized cepstral coefficients(MRPNCC)are proposed as a new feature to enhance the speech intelligibility for hearing impaired.The new feature is constructed by combining four cepstrum at different time–frequency(T–F)resolutions in order to capture both the local and contextual information.MRPNCC vectors and binary masking labels calculated by signals passed through gammatone filterbank are used to train support vector machine(SVM)classifier,which aim to identify the binary masking values of the T–F units in the enhancement stage.The enhanced speech is synthesized by using the estimated masking values and wiener filtered T–F unit.Objective experimental results demonstrate that the proposed feature is superior to other comparing features in terms of HIT-FA,STOI,HASPI and PESQ,and that the proposed algorithm not only improves speech intelligibility but also improves speech quality slightly.Subjective tests validate the effectiveness of the proposed algorithm for hearing impaired.

Study on threshold segmentation of multi-resolution 3D human brain CT image

In order to effectively improve the pathological diagnosis capability and feature resolution of 3D human brain CT images,a threshold segmentation method of multi-resolution 3D human brain CT image based on edge pixel grayscale feature decomposition is proposed in this paper.In this method,first,original 3D human brain image information is collected,and CT image filtering is performed to the collected information through the gradient value decomposition method,and edge contour features of the 3D human brain CT image are extracted.Then,the threshold segmentation method is adopted to segment the regional pixel feature block of the 3D human brain CT image to segment the image into block vectors with high-resolution feature points,and the 3D human brain CT image is reconstructed with the salient feature point as center.Simulation results show that the method proposed in this paper can provide accuracy up to 100%when the signal-to-noise ratio is 0,and with the increase of signal-to-noise ratio,the accuracy provided by this method is stable at 100%.Comparison results show that the threshold segmentation method of multi-resolution 3D human brain CT image based on edge pixel grayscale feature decomposition is signicantly better than traditional methods in pathological feature estimation accuracy,and it effectively improves the rapid pathological diagnosis and positioning recognition abilities to CT images.

A MULTI-RESOLUTION SPECTRUM SENSING (MRSS) SCHEME UNDER MEASUREMENT-BASED CHANNEL MODELS IN COGNITIVE RADIO

Spectrum sensing is one of the key technologies in Cognitive Radios(CRs).Previous works are accomplished under simple channel models,which may lead to unreliable results when it applied to the over-the-air systems.In this paper,we investigate the performance of a Multi-Resolution Spectrum Sensing(MRSS) algorithm under measurement-based channel models in China.MRSS is a wavelet based algorithm which is suitable for non-stationary,wideband signal analysis.Using statistical mod-eling,measurement-based channel models are presented under typical urban and suburban scenarios in Shanghai,China.Then,the performance of the MRSS algorithm is evaluated under the measure-ment-based channel models.Simulation results show that,using MRSS,the performance is always better in the scenarios where Line-Of-Sight(LOS) path exist;also,in LOS scenarios,rich scattering effect helps to increase the performance.

Multi-Resolution Fourier Analysis Part I: Fundamentals

In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequality). In the forthcoming parts of this series, multi-resolution Fourier performances are observed, applied to short signals and extended to time-frequency analysis.

Multi-Resolution Fourier Analysis Part II: Missing Signal Recovery and Observation Results

In this paper, we report application procedures and observed results of multi-resolution Fourier analysis proposed in the first part of this series. Missing signal recovery derived from multi-resolution theory is developed. It is shown that multi-resolution Fourier analysis enhances dramatically performances of Fourier spectra suffering limitations traced to implicit time windowing. Observed frequency resolutions, improvement of frequency estimations, contraction of spectral leakage and recovery of missing parts of finite duration signals are in accordance with theoretical predictions.