Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,...Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.展开更多
提出了一种在梯度域中进行无缝图像处理的方法.在一般的整体变分模型中引入待处理区域的梯度场,得到一个扩展的整体变分模型,称为梯度场整体变分(gradient field totalvariation,GFTV)模型.无缝处理通过最小化模型函数来实现.基于GFTV...提出了一种在梯度域中进行无缝图像处理的方法.在一般的整体变分模型中引入待处理区域的梯度场,得到一个扩展的整体变分模型,称为梯度场整体变分(gradient field totalvariation,GFTV)模型.无缝处理通过最小化模型函数来实现.基于GFTV模型的方法可应用于以下无缝图像处理:在图像中无缝地插入新的目标;无缝地修改图像中某个区域的纹理、光照等外观;图像的无缝拼接等.展开更多
基金Raymond Honfu Chan’s research was supported in part by Hong Kong Research Grants Council(HKRGC)General Research Fund(No.CityU12500915,CityU14306316)HKRGC Collaborative Research Fund(No.C1007-15G)+2 种基金HKRGC Areas of Excellence(No.AoE/M-05/12)Hai-Xia Liang’s research was supported partly by the Natural Science Foundation of Jiangsu Province(No.BK20150373)partly by Xi’an Jiaotong-Liverpool University Research Enhancement Fund(No.17-01-08).
文摘Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.
文摘提出了一种在梯度域中进行无缝图像处理的方法.在一般的整体变分模型中引入待处理区域的梯度场,得到一个扩展的整体变分模型,称为梯度场整体变分(gradient field totalvariation,GFTV)模型.无缝处理通过最小化模型函数来实现.基于GFTV模型的方法可应用于以下无缝图像处理:在图像中无缝地插入新的目标;无缝地修改图像中某个区域的纹理、光照等外观;图像的无缝拼接等.
