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Application of multi-resolution analysis in sonar image denoising

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Journal of Systems Engineering and Electronics 2008年第6期19卷 1082-1089页

作者： Shang Zhengguo Zhao Chunhui Wan Jian Coll. of Information & Communication Engineering Harbin Engineering Univ. Harbin 150001 P. R. China

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.

关键词： multi-resolution analysis wavelet transform ridgelet transform cycle sample adaptive denoisingenergy delamination

multi-resolution analysis of Density Fluctuation of Coherent Structures About Supersonic Flow over VG

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Chinese Journal of Aeronautics 2012年第2期25卷 173-181页

作者： WANG Dengpan ZHAO Yuxin XIA Zhixun WANG Qinghua HUANG Xu Science and Technology on Scramjet Laboratory National University of Defense Technology Changsha 410073 China The ThirdInstitute the SecondArtillery Equipment Academy Beijing 100085 China

The density field around a vortex generator （VG） in supersonic flow is studied with a nanoparticle-based planar laser scattering （NPLS） method. Based on the calibration, i.e., the density distribution of the supersonic flow around a wedge, the density field of a supersonic VG is measured. According to movement characteristics of coherent structure in VG’s flow fields and the basic concepts of wavelet, the density fluctuating signals and multi-resolution characteristics of density field images are studied. The multi-resolution characteristics of density fluctuation can be analyzed with wavelet transformation of NPLS images. The wavelet approximate coefficients of density fluctuating signals exhibit their characteristics at different scales, and the corresponding detail coefficients show the difference of diverse layer smooth approximation in some way. Based on 2D wavelet decomposition and reconstruction of density field images, the approximate and detail signals at different scales are studied, and the coherent structures at different scales are extracted and analyzed.

关键词： vortex generator nanoparticle-based planar laser scattering coherent structure density fluctuation multi-resolution analysis

Capitalizing on Superconvergence for More Accurate multi‑resolution Discontinuous Galerkin Methods

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Communications on Applied Mathematics and Computation 2022年第2期4卷 417-436页

作者： Jennifer K.Ryan Applied Mathematics and Statistics Colorado School of MinesGoldenCO 80401USA

This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.

关键词： multi-resolution analysis multi-wavelets Discontinuous Galerkin Smoothness-Increasing Accuracy-Conserving(SIAC) Post-processing Superconvergence Accuracy enhancement

h-ADAPTIVE analysis BASED ON MESHLESS LOCAL PETROV-G ALERKIN METHOD WITH B SPLINE WAVELET FOR PLATES AND SHELLS

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Acta Mechanica Solida Sinica 2009年第4期22卷 337-346页

作者： Di Li Zhongqin Lin School of Transportation and Vehicle Engineering Shandong University of Technology Zibo 255049 China School of Mechanical Engineering Shanghai Jiaotong University Shanghai 200030 China

Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified.

关键词： meshless methods meshless local Petrov-Galerkin method multi-resolution analysis adaptive analysis plate and shell

Uniform Convergence of Wavelet Solution to the Sideways Heat Equation

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Acta Mathematica Sinica,English Series 2010年第10期26卷 1981-1992页

作者： Jin Ru WANG Department of Applied Mathematics Beijing University of Technology Beijing 100124 P. R. China

We consider the problem uxx（x, t） = ut（x, t）, 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g（t） is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g（t） can produce a big alteration on its solution （if it exists）. We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren＇t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].

关键词： Sideways heat equation multi-resolution analysis Meyer wavelet solution

Uncovering network traffic anomalies based on their sparse distributions

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Science China(Information Sciences) 2014年第9期57卷 256-266页

作者： CHENG GuoZhen CHEN HongChang CHENG DongNian ZHANG Zhen LAN JuLong National Digital Switching System Engineering and Technological Research Center

Characterizing network traffic with higher-dimensional features results in increased complexity of most detectors and classifiers for identifying traffic anomalies.Several key observations from existing studies confirm that network anomalies are typically distributed in a sparse way,with each anomaly essentially characterized by its lower-dimensional features.Based on this important finding,we exploit sparsity in designing a novel detection method for anomalies that ignores redundancies that are dynamically filtered from the feature sets and accurately classifies anomalies.Comparison of our method with three well known techniques shows a10%improvement in accuracy with an O(n)complexity of the classifier.

关键词： anomaly detection feature filtering multi-resolution analysis sparse distribution

multi-resolution EMD and classscatter matrix extracting of tank sound

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Journal of Beijing Institute of Technology 2012年第1期21卷 91-95页

作者：张万君吴晓颖王新 Department of Weapon Engineering Academy of Armored Force Engineering of PLA

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.

关键词： multi-resolution analysis EMD method sound feature extraction class scatter matrix

Minimum-energy wavelet frame on the interval

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Science in China(Series F) 2008年第10期51卷 1547-1562页

作者： GAO XiePing CAO ChunHong College of Information and Engineering Xiangtan University Xiangtan 411105 China

The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows： 1） give the definition of interval minimum-energy wavelet frame; 2） give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3） present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4） give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],

关键词： scaling function multi-resolution analysis wavelet on the interval frame minimum-energy

Modification of multiple Knot B-Spline Wavelet for Solving (Partially) Dirichlet Boundary Value Problem

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Advances in Applied Mathematics and Mechanics 2012年第6期4卷 799-820页

作者： Fatemeh Pourakbari Ali Tavakoli Department of Mathematics Vali-e-Asr University of RafsanjanIran

A construction of multiple knot B-spline wavelets has been given in[C.K.Chui and E.Quak,Wavelet on a bounded interval,In:D.Braess and L.L.Schumaker,editors.Numerical methods of approximation theory.Basel:Birkhauser Verlag;(1992),pp.57–76].In this work,we first modify these wavelets to solve the elliptic(partially)Dirichlet boundary value problems by Galerkin and Petrov Galerkin methods.We generalize this construction to two dimensional case by Tensor product space.In addition,the solution of the system discretized by Galerkin method with modified multiple knot B-spline wavelets is discussed.We also consider a nonlinear partial differential equation for unsteady flows in an open channel called Saint-Venant.Since the solving of this problem by some methods such as finite difference and finite element produce unsuitable approximations specially in the ends of channel,it is solved by multiple knot B-spline wavelet method that yields a very well approximation.Finally,some numerical examples are given to support our theoretical results.

关键词： Galerkin method semi-orthogonal B-spline wavelet multi-resolution analysis tensor product hyperbolic partial differential equation Saint-Venant equations