CAJ | 학술논문

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。
목적：위정학차쾌속진행저제량희소각도추속CT도상중건，본문제출일충기우분렬Bregman수학방법적긴광가약속적도상중건산법。방법수선선택긴광가（Tight Frame）작위정칙화항，근거압축감지원리건립최소화목표함수，이용분렬Bregman수학방법장구해문제분위3보：（1）사용개진적전향투영산법쾌속계산출투영구진；（2）인입중간량，용분렬Bregman원리장무법직접차분적L1정칙화문제전화위가직접차분적L2정칙화문제，병이용공액제도산법구해；（3）이용분렬Bregman원리중적수축공식경신중간량。결과방진화실제중건적CT도상실험표명，상비우전통적대유정칙화약속적철집투영（POCS）대수질대중건모식，분렬Bregman방법재도상보진화계산시간등방면균취득료상가적효과，병차구유엄범적괄용성。결론재희소각도추속CT도상질대중건조건하，본문제출적방법능구쾌속정학중건출만의적추속CT도상，차도상중건속도화도상질량교철집투영방법유교대제고。
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.