数值计算与计算机应用
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数值计算与计算机应用  2017, Vol. 38 Issue (3): 225-235    DOI:
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基于分数阶型算子的偏微分方程图像修复模型
邹杨
中山大学数学学院, 广州 510275
IMAGE REPAINTING MODEL BASED ON PDE WITH FRACTIONAL OPERATOR
Zou Yang
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
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摘要 本文通过周期型的希尔伯特变换得到拉普拉斯算子的一种表达形式,并给出一个正算子的表达形式.根据该算子和热方程给出一个新方程,并修改成有各项异性的方程,并用该各项异性方程进行数字图像的修复实验.从客观数据和修复效果两方面说明,模型在图像修复方面有一定效果.
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关键词希尔伯特变换   正算子   热传导方程   图像修复     
Abstract: This paper introduces a new kind of Laplace operator by Hilbert transform, then define a positive operator based on this new form. According to this operator and heat equation gives a new equation and modified into anisotropic equation, and the anisotropic equation for the digital image restoration experiment. The data and result show the image repainting model works.
Key wordsHilbert transform   positive Laplace operator   Heat-equation   image inpainting   
收稿日期: 2016-07-12;
引用本文:   
. 基于分数阶型算子的偏微分方程图像修复模型[J]. 数值计算与计算机应用, 2017, 38(3): 225-235.
. IMAGE REPAINTING MODEL BASED ON PDE WITH FRACTIONAL OPERATOR[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(3): 225-235.
 
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