Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, United States of America. Department of Radiology, University of Michigan, Ann Arbor, MI 48109, United States of America.
Phys Med Biol. 2018 Feb 6;63(3):035042. doi: 10.1088/1361-6560/aaa71b.
Most existing PET image reconstruction methods impose a nonnegativity constraint in the image domain that is natural physically, but can lead to biased reconstructions. This bias is particularly problematic for Y-90 PET because of the low probability positron production and high random coincidence fraction. This paper investigates a new PET reconstruction formulation that enforces nonnegativity of the projections instead of the voxel values. This formulation allows some negative voxel values, thereby potentially reducing bias. Unlike the previously reported NEG-ML approach that modifies the Poisson log-likelihood to allow negative values, the new formulation retains the classical Poisson statistical model. To relax the non-negativity constraint embedded in the standard methods for PET reconstruction, we used an alternating direction method of multipliers (ADMM). Because choice of ADMM parameters can greatly influence convergence rate, we applied an automatic parameter selection method to improve the convergence speed. We investigated the methods using lung to liver slices of XCAT phantom. We simulated low true coincidence count-rates with high random fractions corresponding to the typical values from patient imaging in Y-90 microsphere radioembolization. We compared our new methods with standard reconstruction algorithms and NEG-ML and a regularized version thereof. Both our new method and NEG-ML allow more accurate quantification in all volumes of interest while yielding lower noise than the standard method. The performance of NEG-ML can degrade when its user-defined parameter is tuned poorly, while the proposed algorithm is robust to any count level without requiring parameter tuning.
大多数现有的 PET 图像重建方法在图像域中施加非负约束，这在物理上是自然的，但会导致有偏差的重建。对于 Y-90 PET 来说，这种偏差尤其成问题，因为正电子产生的概率低，随机符合分数高。本文研究了一种新的 PET 重建公式，该公式强制投影而不是体素值为非负。该公式允许一些负体素值，从而潜在地减少偏差。与之前报告的允许负值的 NEG-ML 方法不同，新公式保留了经典的泊松统计模型。为了放宽 PET 重建标准方法中嵌入的非负约束，我们使用了交替方向乘子法（ADMM）。由于 ADMM 参数的选择会极大地影响收敛速度，因此我们应用了一种自动参数选择方法来提高收敛速度。我们使用 XCAT 体模的肺到肝切片来研究这些方法。我们模拟了低真实符合计数率和高随机分数，这些分数对应于 Y-90 微球放射栓塞患者成像中的典型值。我们将我们的新方法与标准重建算法和 NEG-ML 及其正则化版本进行了比较。我们的新方法和 NEG-ML 都允许在所有感兴趣的体积中进行更准确的定量，同时产生比标准方法更低的噪声。当 NEG-ML 的用户定义参数调整不佳时，其性能可能会下降，而所提出的算法在不需要参数调整的情况下对任何计数水平都具有鲁棒性。
