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
Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in r...Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.展开更多
The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography（CT） reconstruction. A method employing the image gradient sparsity is often used to reduce t...The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography（CT） reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts.To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated.The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.展开更多
The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterat...The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.展开更多
CT(computed tomography)系统实际应用当中,经常会出现扫描数据不满足数据完备性条件的情况.针对不完全角度重建问题的研究,是目前迭代型算法研究中的一个热点.一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取...CT(computed tomography)系统实际应用当中,经常会出现扫描数据不满足数据完备性条件的情况.针对不完全角度重建问题的研究,是目前迭代型算法研究中的一个热点.一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取得了较好的效果,这其中基于交替方向法(alternating direction method,ADM)的重建算法表现出更好的性能.然而,ADM方法在求解过程中对矩阵求逆的处理效率不高,导致极大的计算开销.本文针对该问题,使用非精确ADM方法,利用线性近似的方式替换掉计算开销较大的项,使得矩阵求逆问题可以通过快速傅里叶变换加速实现.实验结果表明,本文提出的非精确交替方向总变分最小化重建算法与精确ADM重建算法相比,没有明显的精度损失,计算时间缩减30%左右.展开更多
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.
基金Projected supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natura Science Foundation of China(Grant No.61372172)
文摘Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.
基金Project supported by the National Natural Science Foundation of China(Grant No.61372172)
文摘The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography（CT） reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts.To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated.The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.
基金supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natural Science Foundation of China(Grant No.61372172)
文摘The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.
文摘CT(computed tomography)系统实际应用当中,经常会出现扫描数据不满足数据完备性条件的情况.针对不完全角度重建问题的研究,是目前迭代型算法研究中的一个热点.一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取得了较好的效果,这其中基于交替方向法(alternating direction method,ADM)的重建算法表现出更好的性能.然而,ADM方法在求解过程中对矩阵求逆的处理效率不高,导致极大的计算开销.本文针对该问题,使用非精确ADM方法,利用线性近似的方式替换掉计算开销较大的项,使得矩阵求逆问题可以通过快速傅里叶变换加速实现.实验结果表明,本文提出的非精确交替方向总变分最小化重建算法与精确ADM重建算法相比,没有明显的精度损失,计算时间缩减30%左右.
