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Medical Image Compression Based on wavelets with Particle Swarm Optimization

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Computers, Materials & Continua 2021年第5期67卷 1577-1593页

作者： Monagi H.Alkinani E.A.Zanaty Sherif M.Ibrahim Department of Computer Science and Artificial Intelligence Faculty of Computer Science and EngineeringUniversity of JeddahJeddahSaudi Arabi Department of Computer Science Faculty of Computers and InformationSohag UniversitySohagEgypt Department of Computer Science and Mathematics Faculty of ScienceSouth Valley UniversityQenaEgypt

This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding.It transfers images into subband details and approximations using a modified Haar wavelet(MHW),and then applies a threshold.PSO is applied for selecting a particle assigned to the threshold values for the subbands.Nine positions assigned to particles values are used to represent population.Every particle updates its position depending on the global best position(gbest)(for all details subband)and local best position(pbest)(for a subband).The fitness value is developed to terminate PSO when the difference between two local best(pbest)successors is smaller than a prescribe value.The experiments are applied on five different medical image types,i.e.,MRI,CT,and X-ray.Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio(PSNR)and compression ratio(CR)points of views.

关键词： Image compression wavelets Haar wavelet particle swarm algorithm medical image compression PSNR and CR

wavelets and Optical Flow Motion Estimation

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 116-137页

作者： P.Dérian P.Héas C.Herzet E.Mémin Departments of Physics and Geosciences California State University ChicoChicoCA 95929-0555USA INRIA Rennes-Bretagne Atlantique Campus de Beaulieu35042 Rennes CEDEXFrance

This article describes the implementation of a simple wavelet-based optical-flow motion estimator dedicated to continuous motions such as fluid flows. The waveletrepresentation of the unknown velocity field is considered. This scale-space representation, associated to a simple gradient-based optimization algorithm, sets up a welldefined multiresolution framework for the optical flow estimation. Moreover, a verysimple closure mechanism, approaching locally the solution by high-order polynomialsis provided by truncating the wavelet basis at fine scales. Accuracy and efficiency of theproposed method is evaluated on image sequences of turbulent fluid flows.

关键词： wavelets optical flow motion estimation large displacements fluid flows

wavelets with Differential Relation

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Acta Mathematica Sinica,English Series 2011年第5期27卷 1011-1022页

作者： Zhi-Tao CHUANG Youming LIU Department of Applied Mathematics Beijing University of Technology Beijing 100124 P. R. China

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli＇s work.

关键词： Differential relation interpolation wavelets scaling functions symmetry

Assessment of distortion in watermarked geospatial vector data using different wavelets

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Geo-Spatial Information Science 2015年第2期18卷 124-133页

作者： Sangita ZOPE-CHAUDHARI Parvatham VENKATACHALAM Krishna Mohan BUDDHIRAJU Centre of Studies in Resources Engineering Indian Institute of Technology BombayMumbaiIndia

With the rapid growth of the Internet,the copyright protection problem occurs frequently,and unauthorized copying and distributing of geospatial data threaten the investments of data producers.Digital watermarking is a possible solution to solve this issue.However,watermarking causes modifications in the original data resulting in distortion and affects accuracy,which is very important to geospatial vector data.This article provides distortion assessment of watermarked geospatial data using wavelet-based invisible watermarking.Eight wavelets at different wavelet decomposition levels are used for accuracy evaluation with the help of error measures such as maximum error and mean square error.Normalized correlation is used as a similarity index between original and extracted watermark.It is observed that the increase in the strength of embedding increases visual degradation.Haar wavelet outperforms the other wavelets,and the third wavelet decomposition level is proved to be optimal level for watermarking.

关键词： digital watermarking geospatial vector data wavelets discrete wavelet transform(DWT) distortion

Some Generalized q-Bessel Type wavelets and Associated Transforms

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Analysis in Theory and Applications 2018年第1期34卷 57-76页

作者： Imen Rezgui Anouar Ben Mabrouk Algerba Number Theory and Nonlinear Analysis Research UnitUR11ES50Department of MathematicsFaculty of Sciences Department of Mathematics Higher Institute of Applied Mathematics and InformaticsStreet of Assad Ibn AlfouratKairouan University Department of Mathematics Faculty of SciencesUniversity of Tabuk

In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.

关键词： wavelets Besel function q-Bessel function modified Bessel functions generalizedq-Bessel functions q-Bessel wavelets.

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artifi cial and historic records

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Earthquake Engineering and Engineering Vibration 2009年第2期8卷 189-206页

作者： P.D. Spanos A. Giaralis Li Jie Rice University Houston TX 77005-1827 USA Department of Civil and Environmental Engineering Rice University Houston TX 77005-1827 USA Institute of Civil Engineering Tongji University Shanghai 200092 China

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum （EPS）. Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average （ARMA） filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals＇ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.

关键词： design spectrum Chinese aseismic code artificial accelerograms evolutionary power spectrum peak factor recorded accelerograms wavelets

wavelets and Geometric Structure for Function Spaces

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Acta Mathematica Sinica,English Series 2004年第2期20卷 357-366页

作者： QiXiangYANG DepartmentofMathematics WuhanUniversityWuhan430072P.R.China

With Littlewood–Paley analysis, Peetre and Triebel classified, systematically, almost all the usual function spaces into two classes of spaces: Besov spaces and Triebel–Lizorkin spaces ; but the structure of dual spaces of is very different from that of Besov spaces or that of Triebel–Lizorkin spaces, and their structure cannot be analysed easily in the Littlewood–Paley analysis. Our main goal is to characterize in tent spaces with wavelets. By the way, some applications are given: (i) Triebel–Lizorkin spaces for p = ∞ defined by Littlewood–Paley analysis cannot serve as the dual spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations among these above spaces and some relations among and L 1 are studied.

关键词： Triebel–Lizorkin spaces Dual spaces wavelets

wavelets and Continuous Wavelet Transform for Autostereoscopic Multiview Images

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Journal of Electrical Engineering 2016年第1期4卷 19-23页

作者： Vladimir Saveljev Dept. of Inform. Display Engineering Hanyang University Seoul 133-791 Korea Imaging Media Research Center KIST Seoul 136-791 Korea

Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays were introduced. In the current paper, we propose the wavelets to analyze such images. The wavelets are built on these reference functions as on the scaling functions of the wavelet analysis. The continuous wavelet transform was successfully applied to the testing wireframe binary objects. The restored locations correspond to the structure of the testing wireframe binary objects.

关键词： 3D display autostereoscopic display integral imaging multiview image processing wavelets

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

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Acta Mathematica Scientia 2009年第5期29卷 1251-1266页

作者：刘和平刘宇王海辉 LMAM School of Mathematical Sciences Peking University Department of Mathematics and Mechanics School of Applied Science University of Science and Technology Beijing Department of Applied Mathematics Beihang University

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 ... 详细信息

关键词： Heisenberg group multiresolution analysis wavelets self-similar tilings