Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA.
Med Phys. 2010 Sep;37(9):5113-25. doi: 10.1118/1.3481510.
This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements.
The authors cast the reconstruction as a compressed sensing problem based on l1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov.
The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging.
It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.
本文研究了从一组欠采样且可能存在噪声的投影测量中重建锥束 CT（CBCT）图像的问题。
作者将重建问题表述为基于 l1 范数最小化的压缩感知问题，同时对 CBCT 投影数据进行基于统计加权最小二乘的约束。为了准确建模，使用 CBCT 投影数据的噪声特性来确定每个投影测量的相对重要性。为了解决压缩感知问题，作者采用了一种最小化全变差范数的方法，使用由 Nesterov 开发的一阶方法满足规定的测量一致性水平。
由于迭代前向和后向投影的方法，该方法可以快速收敛到最优解，而无需过多的内存需求。通过一系列数字和实验体模研究验证了所提出算法的性能。结果表明，通过使用所提出的方法可以从欠采样和可能存在噪声的投影数据中重建高质量的 CBCT 图像。稀疏采样和降低 X 射线管电流（即噪声投影数据）都会导致 CBCT 成像中的辐射剂量降低。
当处理稀疏且可能存在噪声的 CBCT 投影视图时，压缩感知算法的性能优于传统算法。
