Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
Med Phys. 2012 Feb;39(2):589-602. doi: 10.1118/1.3673775.
Positron emission tomography (PET) is a noninvasive molecular imaging tool with various clinical and preclinical applications. The polygonal structure of small-diameter PET scanners that are designed for specific purposes can lead to gaps between the detector modules and result in loss of PET data during measurement. In the current study, the authors applied the compressed sensing (CS)-based total variation (TV) minimization method to PET image reconstructions to reduce the artifacts caused by gaps in small-diameter PET systems.
The first step in each iteration estimates whether an image is consistent with the measured PET data using the existing common reconstruction algorithms (ART, OSEM, and RAMLA). The second step recovers sparsity in the gradient domain of the image by minimizing the TV of an estimated image. The authors evaluated the gap-compensable reconstruction algorithms with uniform disk and Shepp-Logan phantoms by simulating sinograms which contained Poisson random noise and a data loss due to detector gaps. In addition, these methods were applied to real high resolution research tomography (HRRT)-like sinograms of human brain and uniform phantom. A comparison with other methods for gap compensation prior to or during image reconstruction was also made. Quantitative evaluations were performed by computing the uniformity, root mean squared error, and difference between the reconstructed images of nongapped and gapped sinograms.
The simulation results showed that the gap-compensable methods incorporating TV minimization could control gap artifacts, as well as Poisson random noise. In particular, OSEM-TV and RAMLA-TV showed distinct potential via the properties of convergence and robustness to different noise levels and gap angle.
A TV minimization strategy incorporated into commonly used PET reconstruction algorithms was useful for reducing the occurrence of artifacts due to gaps between detector modules in small-diameter PET scanners.
正电子发射断层扫描（PET）是一种具有多种临床和临床前应用的非侵入性分子成像工具。为特定目的而设计的小直径 PET 扫描仪的多边形结构可能导致探测器模块之间存在间隙，从而导致在测量过程中丢失 PET 数据。在当前的研究中，作者将基于压缩感知（CS）的全变差（TV）最小化方法应用于 PET 图像重建中，以减少小直径 PET 系统中间隙引起的伪影。
每次迭代的第一步是使用现有的常用重建算法（ART、OSEM 和 RAMLA）来评估图像是否与测量的 PET 数据一致。第二步通过最小化估计图像的 TV 来恢复图像梯度域中的稀疏性。作者通过模拟包含泊松随机噪声和由于探测器间隙导致的数据丢失的正弦图，使用均匀圆盘和 Shepp-Logan 体模来评估有间隙补偿重建算法。此外，还将这些方法应用于真实的高分辨率研究断层摄影术（HRRT）样本人脑和均匀体模的正弦图。还比较了在图像重建之前或期间进行间隙补偿的其他方法。通过计算非间隙和有间隙正弦图的重建图像的均匀性、均方根误差和差异来进行定量评估。
模拟结果表明，结合 TV 最小化的有间隙补偿方法可以控制间隙伪影以及泊松随机噪声。特别是 OSEM-TV 和 RAMLA-TV 通过收敛性和对不同噪声水平和间隙角度的稳健性表现出明显的潜力。
将 TV 最小化策略纳入常用的 PET 重建算法中，有助于减少小直径 PET 扫描仪中探测器模块之间间隙引起的伪影的发生。
