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
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
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
在基于样例的图像修复算法中,由于优先权公式的计算容易受图像局部噪声和细小纹理的干扰,导致修复顺序错乱;而在搜索最优匹配块时,因忽略了图像块内部的结构影响,可能导致误匹配。针对以上问题提出了一种基于图像的结构-纹理分解及局部...在基于样例的图像修复算法中,由于优先权公式的计算容易受图像局部噪声和细小纹理的干扰,导致修复顺序错乱;而在搜索最优匹配块时,因忽略了图像块内部的结构影响,可能导致误匹配。针对以上问题提出了一种基于图像的结构-纹理分解及局部总变分最小化的图像修复模型。首先,根据对数总变分最小化模型,将待修复图像进行结构-纹理分解,得到图像的结构分量,并利用图像的结构分量来计算待修复点优先权,使优先权的计算排除局部纹理干扰而更具鲁棒性;其次,将优先权的计算改进为数据项和置信项的加权和,避免了乘积效应,确保数据项一直发挥作用,减少因修复顺序不合理造成的错误匹配;最后,根据图像的局部总变分最小化原则,将图像块的最优匹配转换为0-1优化问题,确保图像修复后的局部结构一致性。与3组参考文献的5组对比实验结果表明,峰值信噪比(PSNR)提高了1.12~3.56 d B,结构相似性指数提高了0.02~0.04。所提模型更好地遵循了修复优先性原则,具有更强的保持图像局部结构一致性的能力,改善了修复图像的视觉效果,适用于复杂结构的大面积毁损的图像的修复。展开更多
Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a ...Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.展开更多
A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to ...A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.展开更多
The Chan-Vese method of active contours without edges[11]has been used successfully for segmentation of images.As a variational formulation,it involves the solution of a fully nonlinear partial differential equation w...The Chan-Vese method of active contours without edges[11]has been used successfully for segmentation of images.As a variational formulation,it involves the solution of a fully nonlinear partial differential equation which is usually solved by using time marching methods with semi-implicit schemes for a parabolic equation;the recent method of additive operator splitting[19,36]provides an effective acceleration of such schemes for images of moderate size.However to process images of large size,urgent need exists in developing fast multilevel methods.Here we present a multigrid method to solve the Chan-Vese nonlinear elliptic partial differential equation,and demonstrate the fast convergence.We also analyze the smoothing rates of the associated smoothers.Based on our numerical tests,a surprising observation is that our multigrid method is more likely to converge to the global minimizer of the particular non-convex problem than previously unilevel methods which may get stuck at local minimizers.Numerical examples are given to show the expected gain in CPU time and the added advantage of global solutions.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
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.
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。
文摘在基于样例的图像修复算法中,由于优先权公式的计算容易受图像局部噪声和细小纹理的干扰,导致修复顺序错乱;而在搜索最优匹配块时,因忽略了图像块内部的结构影响,可能导致误匹配。针对以上问题提出了一种基于图像的结构-纹理分解及局部总变分最小化的图像修复模型。首先,根据对数总变分最小化模型,将待修复图像进行结构-纹理分解,得到图像的结构分量,并利用图像的结构分量来计算待修复点优先权,使优先权的计算排除局部纹理干扰而更具鲁棒性;其次,将优先权的计算改进为数据项和置信项的加权和,避免了乘积效应,确保数据项一直发挥作用,减少因修复顺序不合理造成的错误匹配;最后,根据图像的局部总变分最小化原则,将图像块的最优匹配转换为0-1优化问题,确保图像修复后的局部结构一致性。与3组参考文献的5组对比实验结果表明,峰值信噪比(PSNR)提高了1.12~3.56 d B,结构相似性指数提高了0.02~0.04。所提模型更好地遵循了修复优先性原则,具有更强的保持图像局部结构一致性的能力,改善了修复图像的视觉效果,适用于复杂结构的大面积毁损的图像的修复。
基金Supported by the National Natural Science Foundation of China Youth Fund(No.61807029)Natural Science Foundation of Hebei Province(No.F2019203427).
文摘Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.
文摘A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.
文摘The Chan-Vese method of active contours without edges[11]has been used successfully for segmentation of images.As a variational formulation,it involves the solution of a fully nonlinear partial differential equation which is usually solved by using time marching methods with semi-implicit schemes for a parabolic equation;the recent method of additive operator splitting[19,36]provides an effective acceleration of such schemes for images of moderate size.However to process images of large size,urgent need exists in developing fast multilevel methods.Here we present a multigrid method to solve the Chan-Vese nonlinear elliptic partial differential equation,and demonstrate the fast convergence.We also analyze the smoothing rates of the associated smoothers.Based on our numerical tests,a surprising observation is that our multigrid method is more likely to converge to the global minimizer of the particular non-convex problem than previously unilevel methods which may get stuck at local minimizers.Numerical examples are given to show the expected gain in CPU time and the added advantage of global solutions.
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。
