河南理工大学学报（自然科学版）2018，Vol.37Issue(3)：150-156,7.DOI:10.16186/j.cnki.1673-9787.2018.03.22
一种基于微小区域的TV双调和型偏微分方程图像修复方法
A TV harmonic type PDE approach of image inpainting based on observation on a meager domain
摘要
Abstract
We present a new TV-PDE approach of image inpainting based on an incomplete observation of the blurred image.The method is proposed starts from a related variational problem as well as considered in the Sobolev distribution space H-1 (Ω).Its Euler-Lagrange equation is a nonlinear bi-harmonic elliptic diffusion equation related to porous media equation.The equation is belong to a minimization problem.The biharmonic elliptic boundary value problem is used to obtain the generalized solution under the Euler-Lagrange optimal condition.The advantage of the approach is that the observation f can be taken as a distribution with support in a finite number of pointsk { (X(e),yh) }(e),hn,m=1.This means that it can be applied to the image inpainting for a subdomain with zero Lebesgue measure.Steady scale space solutions and the least squares method are used for numerical simulation.We evaluate analog images from three aspects:peak signal to noise ratio(PSNR),structural similarity index and visual intuition.The simulation experiments of nontexture image show that the proposed algorithm can make full use of the existing information adjacent pixels and has better performance of inpainting.The algorithm is suitable for small defect cases.In the process of restoration,this method protects the edge feature,avoids the step effect and improves the visual quality significantly.关键词
图像修复/变分偏微分方程/平均结构相似度/欧拉-拉格朗日方程Key words
image inpainting/variational partial differential equation/mean structural similarity index/Euler-Lagrange分类
自科综合引用本文复制引用
孙俊岭,杨杰..一种基于微小区域的TV双调和型偏微分方程图像修复方法[J].河南理工大学学报（自然科学版）,2018,37(3):150-156,7.基金项目
国家自然科学基金-河南省人才培养联合基金资助项目(U1404103) （U1404103）
