Alessio Adam, Sauer Ken, Kinahan Paul
Department of Radiology, University of Washington Medical Center, Seattle, WA 98195-6004, USA.
Phys Med Biol. 2006 Jan 7;51(1):77-93. doi: 10.1088/0031-9155/51/1/006. Epub 2005 Dec 15.
Fully 3D PET data are often rebinned into 2D data sets in order to avoid computationally intensive fully 3D reconstruction. Then, conventional 2D reconstruction techniques are employed to obtain images from the rebinned data. In a common scenario, 2D filtered back projection (FBP) is applied to Fourier rebinned (FORE) data. This approach is suboptimal because FBP is based on an idealized mathematical model of the data and cannot account for the statistical structure of data and noise. FORE data contain some blur in all three dimensions in comparison to conventional 2D PET data. In this work, we propose methods for approximating this blur in the sinogram domain due to FORE through its point spread function (PSF). We also explore simple methods for deconvolving the rebinned data with this PSF to restore it to a more ideal state prior to FBP. Our results show that deconvolution of the approximate transaxial PSF yields no improvement. When low image noise levels are required for detection tasks, the deconvolution of the axial PSF does not provide adequate resolution or quantitative benefits to justify its application. When accurate quantitation is required and higher noise levels are acceptable, the deconvolution of the axial PSF leads to considerable gains (30%) in accuracy over conventional FORE+FBP at matched noise levels.
为避免计算量巨大的全三维重建，完整的三维正电子发射断层扫描（PET）数据常被重新组合为二维数据集。然后，采用传统的二维重建技术从重新组合的数据中获取图像。在常见情况下，二维滤波反投影（FBP）应用于傅里叶重新组合（FORE）数据。这种方法并不理想，因为FBP基于理想化的数据数学模型，无法考虑数据和噪声的统计结构。与传统的二维PET数据相比，FORE数据在所有三个维度上都存在一些模糊。在这项工作中，我们提出了一些方法，通过其点扩散函数（PSF）在正弦图域中近似FORE造成的这种模糊。我们还探索了用此PSF对重新组合的数据进行去卷积的简单方法，以便在FBP之前将其恢复到更理想的状态。我们的结果表明，对近似横向PSF进行去卷积没有带来改善。当检测任务需要低图像噪声水平时，对轴向PSF进行去卷积并不能提供足够的分辨率或定量优势来证明其应用的合理性。当需要精确量化且可接受较高噪声水平时，在匹配噪声水平下，对轴向PSF进行去卷积比传统的FORE + FBP在精度上有显著提高（30%）。
