Cho Sanghee, Li Quanzheng, Ahn Sangtae, Bai Bing, Leahy Richard M
Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA.
IEEE Trans Med Imaging. 2007 Mar;26(3):347-58.
We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully three-dimensional (3-D) positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a two-dimensional (2-D) projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing line of responses (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.
我们描述了一种基于逆傅里叶重排的快速前向和后向投影器对，用于全三维（3-D）正电子发射断层扫描（PET）的迭代图像重建。该投影器对用作因式分解系统矩阵的一部分，该矩阵通过使用移位可变正弦图模糊核来考虑探测器对响应，从而将傅里叶重排的计算优势与使用精确系统模型的迭代重建相结合。前向投影器由一个二维（2-D）投影器组成，它将3-D图像映射到2-D直接正弦图，然后是精确的逆重排，将2-D映射到全3-D正弦图。后向投影器实现为前向投影器的转置，并且与真正的精确重排算子不同，因为它不需要重新投影来计算缺失的响应线（LOR）。我们补偿了在使用逆傅里叶重排的圆柱形PET扫描仪中出现的两种不准确性：1）径向采样不均匀和2）单个倾斜正弦图中径向方向上的倾斜角不恒定。我们研究了这些校正对正弦图准确性和重建图像质量的影响。我们评估了新投影器对在模拟和体内数据的最大后验（MAP）重建中的性能。与全3-D几何投影器相比，新投影器在视野边缘处的分辨率仅略有损失，并且计算量减少了一个数量级。
