Extremely low-dose CT acquisitions used for PET attenuation correction have high levels of noise and potential bias artifacts due to photon starvation. This work explores the use of a priori knowledge for iterative image reconstruction of the CT-based attenuation map. We investigate a maximum a posteriori framework with cluster-based multinomial penalty for direct iterative coordinate decent (dICD) reconstruction of the PET attenuation map. The objective function for direct iterative attenuation map reconstruction used a Poisson log-likelihood data fit term and evaluated two image penalty terms of spatial and mixture distributions. The spatial regularization is based on a quadratic penalty. For the mixture penalty, we assumed that the attenuation map may consist of four material clusters: air+background, lung, soft tissue, and bone. Using simulated noisy sinogram data, dICD reconstruction was performed with different strengths of the spatial and mixture penalties. The combined spatial and mixture penalties reduced the RMSE by roughly 2 times compared to a weighted least square and filtered backprojection reconstruction of CT images. The combined spatial and mixture penalties resulted in only slightly lower RMSE compared to a spatial quadratic penalty alone. For direct PET attenuation map reconstruction from ultra-low dose CT acquisitions, the combination of spatial and mixture penalties offers regularization of both variance and bias and is a potential method to reconstruct attenuation maps with negligible patient dose. The presented results, using a best-case histogram suggest that the mixture penalty does not offer a substantive benefit over conventional quadratic regularization and diminishes enthusiasm for exploring future application of the mixture penalty.

中文翻译：

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使用基于簇的惩罚直接重建基于 CT 的 PET 衰减校正图像

由于光子不足，用于 PET 衰减校正的极低剂量 CT 采集具有高水平的噪声和潜在的偏差伪影。这项工作探索了使用先验知识对基于 CT 的衰减图进行迭代图像重建。我们研究了最大后验框架，该框架具有基于集群的多项惩罚，用于 PET 衰减图的直接迭代坐标体 (dICD) 重建。直接迭代衰减图重建的目标函数使用泊松对数似然数据拟合项并评估空间和混合分布的两个图像惩罚项。空间正则化基于二次惩罚。对于混合惩罚，我们假设衰减图可能由四个材料簇组成：空气+背景、肺、软组织和骨骼。使用模拟的嘈杂正弦图数据，用不同强度的空间和混合惩罚执行 dICD 重建。与 CT 图像的加权最小二乘和滤波反投影重建相比，组合空间和混合惩罚将 RMSE 降低了大约 2 倍。与单独的空间二次惩罚相比，组合空间和混合惩罚仅导致略低的 RMSE。对于从超低剂量 CT 采集的直接 PET 衰减图重建，空间和混合惩罚的组合提供了方差和偏差的正则化，并且是在患者剂量可忽略不计的情况下重建衰减图的潜在方法。呈现的结果，