Emission image reconstruction for randoms-precorrected PET allowing negative sinogram values.
Emission image reconstruction for randoms-precorrected PET allowing negative sinogram values.
复制标题
随机预校正 PET 的发射图像重建允许负正弦图值。
DOI：
10.1109/tmi.2004.826046
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发表时间：
2004
影响因子：
10.6
通讯作者：
Fessler,JeffreyA
中科院分区：
文献类型：
--
作者：
Ahn,Sangtae;Fessler,JeffreyA
大多数正电子发射断层扫描（PET）发射扫描校正的偶然符合（AC）事件的实时减法延迟窗口符合，只留下随机预校正的数据可用于图像重建。实时随机预校正平均补偿AC事件，但破坏泊松统计。精确的对数似然随机预校正数据是不方便的，所以实际的近似需要最大似然或惩罚似然图像重建。传统的近似涉及将负正弦图值设置为零，这可能引起正系统偏差，特别是对于每射线计数低的扫描。我们提出了新的似然近似，允许负正弦值，而不需要零阈值。与负正弦值，对数似然函数可以是非凹的，复杂的最大化，然而，我们开发的新模型的单调算法，通过修改可分离的抛物面代理和最大似然期望最大化（ML-EM）的方法。这些算法上升到局部最大化的目标函数。分析和仿真结果表明，新的移位泊松（SP）模型几乎没有系统偏差，但保持低方差。尽管其更简单的实现，新的SP执行的鞍点模型，其中已显示出最好的性能（系统偏差和方差）在随机预校正PET发射重建。
Most positron emission tomography (PET) emission scans are corrected for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences, leaving only the randoms-precorrected data available for image reconstruction. The real-time randoms precorrection compensates in mean for AC events but destroys the Poisson statistics. The exact log-likelihood for randoms-precorrected data is inconvenient, so practical approximations are needed for maximum likelihood or penalized-likelihood image reconstruction. Conventional approximations involve setting negative sinogram values to zero, which can induce positive systematic biases, particularly for scans with low counts per ray. We propose new likelihood approximations that allow negative sinogram values without requiring zero-thresholding. With negative sinogram values, the log-likelihood functions can be nonconcave, complicating maximization; nevertheless, we develop monotonic algorithms for the new models by modifying the separable paraboloidal surrogates and the maximum-likelihood expectation-maximization (ML-EM) methods. These algorithms ascend to local maximizers of the objective function. Analysis and simulation results show that the new shifted Poisson (SP) model is nearly free of systematic bias yet keeps low variance. Despite its simpler implementation, the new SP performs comparably to the saddle-point model which has shown the best performance (as to systematic bias and variance) in randoms-precorrected PET emission reconstruction.