Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in prac...Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.展开更多
The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
为了提高现有块压缩感知重构算法的性能,提出了基于全变分和混合变分模型的块压缩感知(简称BCS-TV和BCS-MV)算法。该方法以块为单位进行图像采样,以自然图像正则项的稀疏性为先验条件,通过变型的增广拉格朗日交替方向乘子法(ALM-ADMM),...为了提高现有块压缩感知重构算法的性能,提出了基于全变分和混合变分模型的块压缩感知(简称BCS-TV和BCS-MV)算法。该方法以块为单位进行图像采样,以自然图像正则项的稀疏性为先验条件,通过变型的增广拉格朗日交替方向乘子法(ALM-ADMM),在整幅图像范围内逼近目标函数来重构原始图像。与以前基于一致性块采样的压缩感知工作对比,该算法的PSNR约提高1.5 d B,SSIM约提高0.05,运行速度较稳定,特别适合具有固定传输时延的多媒体数据处理场合。展开更多
基金the National High Technology Research and Development Program of China(Grant No.2012AA011603)
文摘Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
文摘为了提高现有块压缩感知重构算法的性能,提出了基于全变分和混合变分模型的块压缩感知(简称BCS-TV和BCS-MV)算法。该方法以块为单位进行图像采样,以自然图像正则项的稀疏性为先验条件,通过变型的增广拉格朗日交替方向乘子法(ALM-ADMM),在整幅图像范围内逼近目标函数来重构原始图像。与以前基于一致性块采样的压缩感知工作对比,该算法的PSNR约提高1.5 d B,SSIM约提高0.05,运行速度较稳定,特别适合具有固定传输时延的多媒体数据处理场合。
