Kadrmas Dan J
Department of Radiology, Utah Center for Advanced Imaging Research, 729 Arapeen Drive, University of Utah, Salt Lake City, UT 84108, USA.
IEEE Trans Med Imaging. 2008 Aug;27(8):1071-83. doi: 10.1109/TMI.2008.918328.
One of the greatest challenges facing iterative fully-3-D positron emission tomography (PET) reconstruction is the issue of long reconstruction times due to the large number of measurements for 3-D mode as compared to 2-D mode. A rotate-and-slant projector has been developed that takes advantage of symmetries in the geometry to compute volumetric projections to multiple oblique sinograms in a computationally efficient manner. It is based upon the 2-D rotation-based projector using the three-pass method of shears, and it conserves the 2-D rotator computations for multiple projections to each oblique sinogram set. The projector is equally applicable to both conventional evenly-spaced projections and unevenly-spaced line-of-response (LOR) data. The LOR-based version models the location and orientation of the individual LORs (i.e., the arc-correction), providing an ordinary Poisson reconstruction framework. The projector was implemented in C with several optimizations for speed, exploiting the vertical symmetry of the oblique projection process, depth compression, and array indexing schemes which maximize serial memory access. The new projector was evaluated and compared to ray-driven and distance-driven projectors using both analytical and experimental phantoms, and fully-3-D iterative reconstructions with each projector were also compared to Fourier rebinning with 2-D iterative reconstruction. In terms of spatial resolution, contrast, and background noise measures, 3-D LOR-based iterative reconstruction with the rotate-and-slant projector performed as well as or better than the other methods. Total processing times, measured on a single cpu Linux workstation, were approximately 10x faster for the rotate-and-slant projector than for the other 3-D projectors studied. The new projector provided four iterations fully-3-D ordered-subsets reconstruction in as little as 15 s--approximately the same time as FORE + 2-D reconstruction. We conclude that the rotate-and-slant projector is a viable option for fully-3-D PET, offering quality statistical reconstruction in times only marginally slower than 2-D or rebinning methods.
迭代全三维正电子发射断层扫描（PET）重建面临的最大挑战之一是，与二维模式相比，三维模式下由于测量数量众多，导致重建时间较长。现已开发出一种旋转倾斜投影器，它利用几何结构中的对称性，以高效的计算方式计算体积投影，生成多个倾斜正弦图。该投影器基于采用三次剪切法的二维旋转投影器，并且为每个倾斜正弦图集的多个投影保留二维旋转器计算。该投影器同样适用于传统的均匀间隔投影和非均匀间隔响应线（LOR）数据。基于LOR的版本对各个LOR的位置和方向进行建模（即弧线校正），提供一个普通的泊松重建框架。该投影器用C语言实现，并进行了多项速度优化，利用了倾斜投影过程的垂直对称性、深度压缩以及能使串行内存访问最大化的数组索引方案。使用解析和实验体模对新投影器进行了评估，并与射线驱动和距离驱动投影器进行了比较，还将使用每个投影器的全三维迭代重建与二维迭代重建的傅里叶重新组合进行了比较。在空间分辨率、对比度和背景噪声测量方面，基于三维LOR的旋转倾斜投影器迭代重建的性能与其他方法相当或更优。在单个CPU Linux工作站上测量的总处理时间，旋转倾斜投影器比所研究的其他三维投影器快约10倍。新投影器在短短15秒内就能提供四次全三维有序子集重建——大约与FORE + 二维重建所需时间相同。我们得出结论，旋转倾斜投影器是全三维PET的一个可行选择，能提供高质量的统计重建，其时间仅比二维或重新组合方法略长。
