Yu Haiqing, Chen Zhi, Zhang Heye, Wong Kelvin Kian Loong, Chen Yunmei, Liu Huafeng
Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.
Shenzhen Institutes of Advanced Technology, Shenzhen, Guangdong, China.
PLoS One. 2015 Sep 23;10(9):e0138483. doi: 10.1371/journal.pone.0138483. eCollection 2015.
This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).
本文提出了一种用于三维正电子发射断层扫描（PET）的全变差（TV）正则化重建算法。所提出的方法首先采用傅里叶重排算法（FORE），将三维数据重排成一堆普通的二维数据集作为正弦图数据。然后，所得的二维正弦图准备好通过传统的二维重建算法进行重建。鉴于PET图像具有局部逐段恒定的性质，我们引入了基于全变差（TV）的重建方案。更具体地说，我们将二维PET重建问题表述为一个优化问题，其目标函数由重建图像的TV范数和测量重建图像与正弦图之间一致性的数据保真项组成。为了解决由此产生的最小化问题，我们应用了一种称为变步长Bregman算子分裂算法（BOSVS）的有效方法。基于蒙特卡罗模拟数据和真实数据进行了实验作为验证。实验结果表明，所提出的方法比传统的直接傅里叶（DF）方法具有更高的精度（BOSVS中的偏差是DF中的70%，BOSVS中的方差是DF中的80%）。
