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Advancements to the planogram frequency–distance rebinning algorithm
Inverse Problems ( IF 2.1 ) Pub Date : 2010-03-25 , DOI: 10.1088/0266-5611/26/4/045008
Kyle M Champley 1 , Raymond R Raylman , Paul E Kinahan
Affiliation  

In this paper we consider the task of image reconstruction in positron emission tomography (PET) with the planogram frequency-distance rebinning (PFDR) algorithm. The PFDR algorithm is a rebinning algorithm for PET systems with panel detectors. The algorithm is derived in the planogram coordinate system which is a native data format for PET systems with panel detectors. A rebinning algorithm averages over the redundant four-dimensional set of PET data to produce a three-dimensional set of data. Images can be reconstructed from this rebinned three-dimensional set of data. This process enables one to reconstruct PET images more quickly than reconstructing directly from the four-dimensional PET data. The PFDR algorithm is an approximate rebinning algorithm. We show that implementing the PFDR algorithm followed by the (ramp) filtered backprojection (FBP) algorithm in linogram coordinates from multiple views reconstructs a filtered version of our image. We develop an explicit formula for this filter which can be used to achieve exact reconstruction by means of a modified FBP algorithm applied to the stack of rebinned linograms and can also be used to quantify the errors introduced by the PFDR algorithm. This filter is similar to the filter in the planogram filtered backprojection algorithm derived by Brasse et al. The planogram filtered backprojection and exact reconstruction with the PFDR algorithm require complete projections which can be completed with a reprojection algorithm. The PFDR algorithm is similar to the rebinning algorithm developed by Kao et al. By expressing the PFDR algorithm in detector coordinates, we provide a comparative analysis between the two algorithms. Numerical experiments using both simulated data and measured data from a positron emission mammography/tomography (PEM/PET) system are performed. Images are reconstructed by PFDR+FBP (PFDR followed by 2D FBP reconstruction), PFDRX (PFDR followed by the modified FBP algorithm for exact reconstruction) and planogram filtered backprojection image reconstruction algorithms. We show that the PFDRX algorithm produces images that are nearly as accurate as images reconstructed with the planogram filtered backprojection algorithm and more accurate than images reconstructed with the PFDR+FBP algorithm. Both the PFDR+FBP and PFDRX algorithms provide a dramatic improvement in computation time over the planogram filtered backprojection algorithm.

中文翻译:

货架图频率-距离重新组合算法的改进

在本文中,我们考虑使用货架图频率-距离重新组合 (PFDR) 算法在正电子发射断层扫描 (PET) 中进行图像重建的任务。PFDR 算法是一种用于带有面板检测器的 PET 系统的重新组合算法。该算法是在货架图坐标系中推导出来的,货架图坐标系是带有面板检测器的 PET 系统的原生数据格式。重新组合算法对冗余的四维 PET 数据集进行平均以生成三维数据集。可以从这个重新组合的三维数据集重建图像。这一过程使人们能够比直接从四维 PET 数据重建更快地重建 PET 图像。PFDR 算法是一种近似的重新组合算法。我们表明,在来自多个视图的线性图坐标中实施 PFDR 算法,然后是(斜坡)滤波反投影(FBP)算法,可以重建我们图像的滤波版本。我们为该滤波器开发了一个明确的公式,该公式可用于通过应用于重组线图堆栈的修改 FBP 算法实现精确重建,也可用于量化 PFDR 算法引入的误差。该过滤器类似于Brasse等人推导出的planogram过滤反投影算法中的过滤器。使用 PFDR 算法的货架图过滤反投影和精确重建需要完整的投影,这可以使用重投影算法完成。PFDR 算法类似于 Kao 等人开发的重新组合算法。通过在探测器坐标中表达 PFDR 算法,我们提供了两种算法之间的比较分析。使用来自正电子发射乳房 X 线摄影/断层扫描 (PEM/PET) 系统的模拟数据和测量数据进行数值实验。图像由 PFDR+FBP(PFDR 后跟 2D FBP 重建)、PFDRX(PFDR 后跟用于精确重建的修改后的 FBP 算法)和平面图滤波反投影图像重建算法重建。我们表明 PFDRX 算法生成的图像几乎与使用平面图滤波反投影算法重建的图像一样准确,并且比使用 PFDR+FBP 算法重建的图像更准确。
更新日期:2010-03-25
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