Instituto de Física Corpuscular, CSIC/Universitat de València, Valencia, Spain.
Phys Med Biol. 2012 Apr 7;57(7):1759-77. doi: 10.1088/0031-9155/57/7/1759. Epub 2012 Mar 9.
In emission tomography, iterative statistical methods are accepted as the reconstruction algorithms that achieve the best image quality. The accuracy of these methods relies partly on the quality of the system response matrix (SRM) that characterizes the scanner. The more physical phenomena included in the SRM, the higher the SRM quality, and therefore higher image quality is obtained from the reconstruction process. High-resolution small animal scanners contain as many as 10³-10⁴ small crystal pairs, while the field of view (FOV) is divided into hundreds of thousands of small voxels. These two characteristics have a significant impact on the number of elements to be calculated in the SRM. Monte Carlo (MC) methods have gained popularity as a way of calculating the SRM, due to the increased accuracy achievable, at the cost of introducing some statistical noise and long simulation times. In the work presented here the SRM is calculated using MC methods exploiting the cylindrical symmetries of the scanner, significantly reducing the simulation time necessary to calculate a high statistical quality SRM and the storage space necessary. The use of cylindrical symmetries makes polar voxels a convenient basis function. Alternatively, spherically symmetric basis functions result in improved noise properties compared to cubic and polar basis functions. The quality of reconstructed images using polar voxels, spherically symmetric basis functions on a polar grid, cubic voxels and post-reconstruction filtered polar and cubic voxels is compared from a noise and spatial resolution perspective. This study demonstrates that polar voxels perform as well as cubic voxels, reducing the simulation time necessary to calculate the SRM and the disk space necessary to store it. Results showed that spherically symmetric functions outperform polar and cubic basis functions in terms of noise properties, at the cost of slightly degraded spatial resolution, larger SRM file size and longer reconstruction times. However, we demonstrate that post-reconstruction smoothing, usually applied in emission imaging to reduce the level of noise, can produce a spatial resolution degradation of ~50%, while spherically symmetric basis functions produce a degradation of only ~6%, compared to polar and cubic voxels, at the same noise level. Therefore, the image quality trade-off obtained with blobs is higher than that obtained with cubic or polar voxels.
在发射断层成像中，迭代统计方法被认为是实现最佳图像质量的重建算法。这些方法的准确性部分依赖于系统响应矩阵（SRM）的质量，该矩阵描述了扫描仪的特性。SRM 中包含的物理现象越多，SRM 的质量就越高，因此从重建过程中获得的图像质量就越高。高分辨率小动物扫描仪包含多达 10³-10⁴个小晶体对，而视场（FOV）被分为数十万个体素。这两个特征对 SRM 中要计算的元素数量有重大影响。由于可以提高精度，蒙特卡罗（MC）方法作为计算 SRM 的方法而受到欢迎，但代价是引入了一些统计噪声和较长的模拟时间。在本工作中，利用 MC 方法计算 SRM，利用扫描仪的圆柱对称性，显著减少了计算高统计质量 SRM 所需的模拟时间和存储空间。使用圆柱对称性使极体素成为方便的基函数。相比之下，与立方和极体素相比，球对称基函数具有更好的噪声特性。从噪声和空间分辨率的角度比较了使用极体素、极坐标网格上的球对称基函数、立方体素以及重建后滤波的极体素和立方体素的重建图像的质量。这项研究表明，极体素的性能与立方体素一样好，可以减少计算 SRM 所需的模拟时间和存储它所需的磁盘空间。结果表明，球对称函数在噪声特性方面优于极体素和立方体素函数，代价是空间分辨率略有下降，SRM 文件大小增加，重建时间延长。然而，我们证明了重建后平滑处理（通常应用于发射成像以降低噪声水平）会导致空间分辨率下降约 50%，而球对称基函数只会导致空间分辨率下降约 6%，与极体素和立方体素相比，在相同的噪声水平下。因此，与立方体素或极体素相比，使用球形基函数的图像质量权衡更高。
