Noise-weighted FBP (filtered backprojection) algorithm and Bayesian FBP algorithm were developed recently for un-attenuated Radon transform, which have applications in x-ray CT (computed tomography). This paper extends the noise-weighted FBP algorithm to the case of uniformly attenuated Radon transform, and this extended FBP algorithm can be applied in uniformly attenuated SPECT (single photon emission computed tomography). Computer simulations and experimental data demonstrate that the proposed FBP algorithm has similar noise control capability as the iterative ML-EM (maximum likelihood expectation maximization) algorithm. In practice, the attenuator is rarely uniform. A stable FBP algorithm must be developed for non-uniform attenuators before the FBP algorithm can be applied in clinics when attenuation correction is required.

中文翻译：

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用于均匀衰减 SPECT 投影的噪声加权 FBP 算法

噪声加权 FBP（滤波反投影）算法和贝叶斯 FBP 算法最近被开发用于非衰减氡变换，它们在 X 射线 CT（计算机断层扫描）中有应用。本文将噪声加权FBP算法扩展到均匀衰减Radon变换的情况，该扩展FBP算法可应用于均匀衰减SPECT（单光子发射计算机断层扫描）。计算机模拟和实验数据表明，所提出的 FBP 算法具有与迭代 ML-EM（最大似然期望最大化）算法相似的噪声控制能力。实际上，衰减器很少是均匀的。当需要衰减校正时，在将 FBP 算法应用于临床之前，必须为非均匀衰减器开发稳定的 FBP 算法。