Attenuation of noise is a persistent problem in seismic exploration. The authors use conventional denoising method to remove noise which may cause vibration near the discontinuity called pseudo-Gibbs artifact.In order...Attenuation of noise is a persistent problem in seismic exploration. The authors use conventional denoising method to remove noise which may cause vibration near the discontinuity called pseudo-Gibbs artifact.In order to remove the artifact,the study proposed a method combining the seislet transform and total variation minimization. Firstly,the data are converted into the seislet transform domain. Secondly,the hard threshold was used for eliminating the noise and keep useful signal,which is the initial input for the next step. Finally,total variation minimization dealed with denoised data to recover boundary information and further eliminated the noise. Synthetic data examples show that the method has feasibility in eliminating random noise and protecting detailed signal,and also shows better results than the classic f-x deconvolution. The field data example also shows effective in practice. It can remove the noise and preserve the discontinuity signal at the same time.展开更多
Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based pen...Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.展开更多
New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are give...New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.展开更多
基于降低设备制造成本或辐射剂量等目的,计算机断层成像(Computer Tomography,CT)中的一个实际需求是以有限的探测器尺寸来获得更大的视野(Field of View,FOV),通过将探测器放置在横向偏移位置可以有效的扩大FOV。然而,常规的重建算法...基于降低设备制造成本或辐射剂量等目的,计算机断层成像(Computer Tomography,CT)中的一个实际需求是以有限的探测器尺寸来获得更大的视野(Field of View,FOV),通过将探测器放置在横向偏移位置可以有效的扩大FOV。然而,常规的重建算法无法精确重建偏置投影数据,针对这一问题,本文提出了一种基于自适应加权增强总变差最小化的偏置重建模型及CP(Chambolle-Pock)求解算法。具体来说,构建自适应加权增强总变差范数作为正则项,其中自适应权重根据局部增强梯度自适应调整权值,进而设计了一种基于自适应加权增强总变差最小化的偏置重建模型(Weighted Adaptive-weight reinforced Total Variation,WAwrTV),并推导出了相应的CP算法。实验结果表明,所提算法能有效的重建偏置投影数据并提高重建精度,且具有良好的抗噪性能。展开更多
In this paper,we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method.An alternating minimization direction algorithm is then employed.We a...In this paper,we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method.An alternating minimization direction algorithm is then employed.We also prove that it converges strongly to the minimizer of the proposed hybrid model.Finally,some numerical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations.展开更多
空间变化PSF(Space-variant Point Spread Function,SVPSF)图像,即物空间各点的退化随位置的改变而改变的图像,由于其复原技术涉及到多个甚至海量PSF的提取、存储和运算,相对于空间不变PSF(Space-Invariant Point Spread Function,SIPSF...空间变化PSF(Space-variant Point Spread Function,SVPSF)图像,即物空间各点的退化随位置的改变而改变的图像,由于其复原技术涉及到多个甚至海量PSF的提取、存储和运算,相对于空间不变PSF(Space-Invariant Point Spread Function,SIPSF)图像复原要困难得多。目前处理此类图像的主要方法包括空间坐标转换法,等晕区分块复原法,以减少数据存储量,降低计算量,提高收敛速度为目标的直接复原法等。本文回顾了这一课题的研究历史,对目前的研究工作进行了分析和总结,介绍了本实验室提出的结合GRM(Gradient Ringing Metric)评价算法的总变分最小化图像分块复原法,并提出了未来工作关注重点的展望。展开更多
针对全变分模型(total variation,TV)以图像的梯度信息作为去噪的尺度参数,未考虑图像局部纹理的方向性的缺点,提出了一种基于图像局部方向特性的自适应全变分去噪模型(Adaptive directional total variation,ADTV),并推导出该模型的迭...针对全变分模型(total variation,TV)以图像的梯度信息作为去噪的尺度参数,未考虑图像局部纹理的方向性的缺点,提出了一种基于图像局部方向特性的自适应全变分去噪模型(Adaptive directional total variation,ADTV),并推导出该模型的迭代数值求解过程。在该模型中,首先,计算出图像局部方向的角度矩阵。然后,构造与图像纹理方向一致的椭圆区域代替TV模型的圆形区域。最后,通过优化最小化算法迭代求解以获得去噪后图像。通过对比实验证明,本文提出的模型取得了更高的峰值信噪比,去噪过程中更好地增强了图像的细节信息。展开更多
文摘Attenuation of noise is a persistent problem in seismic exploration. The authors use conventional denoising method to remove noise which may cause vibration near the discontinuity called pseudo-Gibbs artifact.In order to remove the artifact,the study proposed a method combining the seislet transform and total variation minimization. Firstly,the data are converted into the seislet transform domain. Secondly,the hard threshold was used for eliminating the noise and keep useful signal,which is the initial input for the next step. Finally,total variation minimization dealed with denoised data to recover boundary information and further eliminated the noise. Synthetic data examples show that the method has feasibility in eliminating random noise and protecting detailed signal,and also shows better results than the classic f-x deconvolution. The field data example also shows effective in practice. It can remove the noise and preserve the discontinuity signal at the same time.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372172 and 61601518)
文摘Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.
文摘New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.
文摘基于降低设备制造成本或辐射剂量等目的,计算机断层成像(Computer Tomography,CT)中的一个实际需求是以有限的探测器尺寸来获得更大的视野(Field of View,FOV),通过将探测器放置在横向偏移位置可以有效的扩大FOV。然而,常规的重建算法无法精确重建偏置投影数据,针对这一问题,本文提出了一种基于自适应加权增强总变差最小化的偏置重建模型及CP(Chambolle-Pock)求解算法。具体来说,构建自适应加权增强总变差范数作为正则项,其中自适应权重根据局部增强梯度自适应调整权值,进而设计了一种基于自适应加权增强总变差最小化的偏置重建模型(Weighted Adaptive-weight reinforced Total Variation,WAwrTV),并推导出了相应的CP算法。实验结果表明,所提算法能有效的重建偏置投影数据并提高重建精度,且具有良好的抗噪性能。
基金supported by RGC 203109,RGC 201508the FRGs of Hong Kong Baptist Universitythe PROCORE-France/Hong Kong Joint Research Scheme sponsored by the Research Grant Council of Hong Kong and the Consulate General of France in Hong Kong F-HK05/08T.
文摘In this paper,we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method.An alternating minimization direction algorithm is then employed.We also prove that it converges strongly to the minimizer of the proposed hybrid model.Finally,some numerical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations.
文摘空间变化PSF(Space-variant Point Spread Function,SVPSF)图像,即物空间各点的退化随位置的改变而改变的图像,由于其复原技术涉及到多个甚至海量PSF的提取、存储和运算,相对于空间不变PSF(Space-Invariant Point Spread Function,SIPSF)图像复原要困难得多。目前处理此类图像的主要方法包括空间坐标转换法,等晕区分块复原法,以减少数据存储量,降低计算量,提高收敛速度为目标的直接复原法等。本文回顾了这一课题的研究历史,对目前的研究工作进行了分析和总结,介绍了本实验室提出的结合GRM(Gradient Ringing Metric)评价算法的总变分最小化图像分块复原法,并提出了未来工作关注重点的展望。
文摘针对全变分模型(total variation,TV)以图像的梯度信息作为去噪的尺度参数,未考虑图像局部纹理的方向性的缺点,提出了一种基于图像局部方向特性的自适应全变分去噪模型(Adaptive directional total variation,ADTV),并推导出该模型的迭代数值求解过程。在该模型中,首先,计算出图像局部方向的角度矩阵。然后,构造与图像纹理方向一致的椭圆区域代替TV模型的圆形区域。最后,通过优化最小化算法迭代求解以获得去噪后图像。通过对比实验证明,本文提出的模型取得了更高的峰值信噪比,去噪过程中更好地增强了图像的细节信息。
