Total variation(TV) is widely applied in image processing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the socalled staircase effect. In order to reduce the staircas...Total variation(TV) is widely applied in image processing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the socalled staircase effect. In order to reduce the staircase effect and preserve the edges when textures of image are extracted, a new image decomposition model is proposed in this paper. The proposed model is based on the total generalized variation method which involves and balances the higher order of the structure. We also derive a numerical algorithm based on a primaldual formulation that can be effectively implemented. Numerical experiments show that the proposed method can achieve a better tradeoff between noise removal and texture extraction, while avoiding the staircase effect efficiently.展开更多
Low-rank matrix decomposition with first-order total variation(TV)regularization exhibits excellent performance in exploration of image structure.Taking advantage of its excellent performance in image denoising,we app...Low-rank matrix decomposition with first-order total variation(TV)regularization exhibits excellent performance in exploration of image structure.Taking advantage of its excellent performance in image denoising,we apply it to improve the robustness of deep neural networks.However,although TV regularization can improve the robustness of the model,it reduces the accuracy of normal samples due to its over-smoothing.In our work,we develop a new low-rank matrix recovery model,called LRTGV,which incorporates total generalized variation(TGV)regularization into the reweighted low-rank matrix recovery model.In the proposed model,TGV is used to better reconstruct texture information without over-smoothing.The reweighted nuclear norm and Li-norm can enhance the global structure information.Thus,the proposed LRTGV can destroy the structure of adversarial noise while re-enhancing the global structure and local texture of the image.To solve the challenging optimal model issue,we propose an algorithm based on the alternating direction method of multipliers.Experimental results show that the proposed algorithm has a certain defense capability against black-box attacks,and outperforms state-of-the-art low-rank matrix recovery methods in image restoration.展开更多
The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differ...The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.展开更多
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
针对低剂量计算机断层扫描(CT)重建图像时出现明显条形伪影的现象,提出一种自适应广义总变分(ATGV)降噪算法。该算法考虑了传统广义总变分(TGV)算法在降噪时模糊图像边缘信息的缺点,把可以有效区分图像平滑区和细节区的直觉模糊熵应用...针对低剂量计算机断层扫描(CT)重建图像时出现明显条形伪影的现象,提出一种自适应广义总变分(ATGV)降噪算法。该算法考虑了传统广义总变分(TGV)算法在降噪时模糊图像边缘信息的缺点,把可以有效区分图像平滑区和细节区的直觉模糊熵应用到传统TGV中,对图像的不同区域进行不同强度的去噪,从而达到保护图像细节的效果。该算法首先采用滤波反投影(FBP)算法得到低剂量CT重建图像;然后利用基于直觉模糊熵的边缘指示函数对传统TGV模型进行改进;最后用改进后的模型对重建图像进行降噪处理。采用Shepp-Logan模型和数字胸腔模型(thorax phantom)仿真低剂量CT重建图像来验证算法的有效性。实验结果表明,所提算法的归一化均方距离(NMSD)和归一化平均绝对距离(NAAD)均比总变分(TV)降噪算法和广义总变分(TGV)降噪算法小,且可分别获得26.90 d B和44.58 d B的峰值信噪比(PSNR)。该算法在去除条形伪影的同时可以较好地保持图像的边缘和细节信息。展开更多
基金supported by the National Natural Science Foundation of China(6127129461301229)+1 种基金the Doctoral Research Fund of Henan University of Science and Technology(0900170809001751)
文摘Total variation(TV) is widely applied in image processing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the socalled staircase effect. In order to reduce the staircase effect and preserve the edges when textures of image are extracted, a new image decomposition model is proposed in this paper. The proposed model is based on the total generalized variation method which involves and balances the higher order of the structure. We also derive a numerical algorithm based on a primaldual formulation that can be effectively implemented. Numerical experiments show that the proposed method can achieve a better tradeoff between noise removal and texture extraction, while avoiding the staircase effect efficiently.
基金Project supported by the National Natural Science Foundation of China(No.62072024)the Outstanding Youth Program of Beijing University of Civil Engineering and Architecture,China(No.JDJQ20220805)the Shenzhen Stability Support General Project(Type A),China(No.20200826104014001)。
文摘Low-rank matrix decomposition with first-order total variation(TV)regularization exhibits excellent performance in exploration of image structure.Taking advantage of its excellent performance in image denoising,we apply it to improve the robustness of deep neural networks.However,although TV regularization can improve the robustness of the model,it reduces the accuracy of normal samples due to its over-smoothing.In our work,we develop a new low-rank matrix recovery model,called LRTGV,which incorporates total generalized variation(TGV)regularization into the reweighted low-rank matrix recovery model.In the proposed model,TGV is used to better reconstruct texture information without over-smoothing.The reweighted nuclear norm and Li-norm can enhance the global structure information.Thus,the proposed LRTGV can destroy the structure of adversarial noise while re-enhancing the global structure and local texture of the image.To solve the challenging optimal model issue,we propose an algorithm based on the alternating direction method of multipliers.Experimental results show that the proposed algorithm has a certain defense capability against black-box attacks,and outperforms state-of-the-art low-rank matrix recovery methods in image restoration.
文摘The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.
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.
文摘针对低剂量计算机断层扫描(CT)重建图像时出现明显条形伪影的现象,提出一种自适应广义总变分(ATGV)降噪算法。该算法考虑了传统广义总变分(TGV)算法在降噪时模糊图像边缘信息的缺点,把可以有效区分图像平滑区和细节区的直觉模糊熵应用到传统TGV中,对图像的不同区域进行不同强度的去噪,从而达到保护图像细节的效果。该算法首先采用滤波反投影(FBP)算法得到低剂量CT重建图像;然后利用基于直觉模糊熵的边缘指示函数对传统TGV模型进行改进;最后用改进后的模型对重建图像进行降噪处理。采用Shepp-Logan模型和数字胸腔模型(thorax phantom)仿真低剂量CT重建图像来验证算法的有效性。实验结果表明,所提算法的归一化均方距离(NMSD)和归一化平均绝对距离(NAAD)均比总变分(TV)降噪算法和广义总变分(TGV)降噪算法小,且可分别获得26.90 d B和44.58 d B的峰值信噪比(PSNR)。该算法在去除条形伪影的同时可以较好地保持图像的边缘和细节信息。
