一种基于分裂Bregman方法求解的锥束CT图像迭代重建

摘要

目的：为精确且快速进行低剂量稀疏角度锥束CT图像重建，本文提出一种基于分裂Bregman数学方法的紧框架约束的图像重建算法。方法首先选择紧框架（Tight Frame）作为正则化项，根据压缩感知原理建立最小化目标函数，利用分裂Bregman数学方法将求解问题分为3步：（1）使用改进的前向投影算法快速计算出投影矩阵；（2）引入中间量，用分裂Bregman原理将无法直接差分的L1正则化问题转化为可直接差分的L2正则化问题，并利用共轭梯度算法求解；（3）利用分裂Bregman原理中的收缩公式更新中间量。结果仿真和实际重建的CT图像实验表明，相比于传统的带有正则化约束的凸集投影（POCS）代数迭代重建模式，分裂Bregman方法在图像保真和计算时间等方面均取得了上佳的效果，并且具有广泛的适用性。结论在稀疏角度锥束CT图像迭代重建条件下，本文提出的方法能够快速精确重建出满意的锥束CT图像，且图像重建速度和图像质量较凸集投影方法有较大提高。%Objective We propose a new iterative reconstruction method based on split-Bregman method with tight frame regularization for effective and accurate reconstruction of the sparse-view cone beam CT image. Methods A tight frame was chosen as the regularization term for the objective function, so that the image reconstruction involves only the minimization of an objective function according to the compressed sensing theory. We utilized the split-Bregman method to tackle the task of minimization in three steps:(1) a fast calculation of the forward projection matrix;(2) introducing an intermediate variable to transform the non-differentiated L1 regularization term into the differentiated L2 regularization problem, and solving the target function using conjugate-gradient method; (3) updating the intermediate variable using shrinkage formula from Bregman method. Results Digital and physical phantom experimental results suggested that our new approach had great advantages in terms of image quality, reconstruction time, and applicability. Conclusion The proposed method can accurately reconstruct CBCT image with limited data to lower the X-ray dose and accelerate the calculation speed in comparison with the POCS method.