标签: Laplace

NumericalinversionofLaplacetransformsbyasimplecurvefittingtechnique

NUMERICALINVERSIONOFTHELAPLACETRANSFORM-ANEXPLICITCLOSED-FORMEXPRESSIONFORTHETIME-DOMAINSOLUTION

改进Laplace的无人机图像边缘检测算法研究

Transforms

Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulseresponsesofthesesystemscannotbearbitrary,butmustbeconsistentwiththesolutionofthesedifferentialequations.Thismeansthattheirimpulseresponsescanonlyconsistofexponentialsandsinusoids.TheLaplacetransformisatechniqueforanalyzingthesespecialsystemswhenthesignalsarecontinuous.Theztransformisasimilartechniqueusedinthediscretecase.CHAPTERTheLaplaceTransform32Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulse……

提出了一种基于小波框架的非局部曲面去噪方法。该方法首先平滑了曲面法线方向上的平均曲率，然后根据基于小波紧框架的变分模型校正了含噪声曲面。变分模型由正则项和保真项构成。其中，正则项为包含小波框架的L1范数项，保真项为离散曲面的平均曲率和点坐标的最小二乘项之和。最后，进行了数值实验验证了所提出模型和算法的有效性和实用性。