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Partial Differential Equations as Three-Dimensional Inverse Problem of Moments 被引量:1
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作者 Maria B. Pintarelli Fernando Vericat 《Journal of Mathematics and System Science》 2014年第10期657-666,共10页
We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = (a1, b1 ) × (a2, b2 ) x (a3, b3 ). We will see that with a common p... We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = (a1, b1 ) × (a2, b2 ) x (a3, b3 ). We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments. 展开更多
关键词 Partial differential equations (pdes) Freholm integral equations generalized moment problem
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ORTHOGONAL-DIRECTIONAL FORWARD DIFFUSION IMAGE INPAINTING AND DENOISING MODEL
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作者 Wu Jiying Ruan Qiuqi An Gaoyun 《Journal of Electronics(China)》 2008年第5期622-628,共7页
In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores t... In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores the damaged information and smoothes the noise in image si-multaneously.The model is morphological invariant which processes image based on the geometrical property.The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions.The cross isophote diffusion part is the TV(Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation.The equivalence between the Helmholtz equation and the inpainting PDEs is proved.The model with the fidelity item which is used in the whole image domain denoises while preserving edges.So the novel model could inpaint and denoise simultaneously.Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper. 展开更多
关键词 Image inpainting Image denoising Partial Differential Equations (pdes) Orthogonal-directional forward diffusion
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