为实现4维动态SPECT图像的快速定量重建，提出了一种用于扇形投影方式下的解析重建算法。该方法首先利用Karhune Loève (KL)变换提取出投影时间序列的相关信息；然后再利用推导至扇形投影方式下的Novikov求逆变换公式，在KL域中对投影分量进行有选择的部分或全部重建；最后通过逆KL变换获得重建图像。实验结果表明，该算法能有效补偿非均匀衰减的影响，其重建图像虽与迭代算法的结果接近，但重建时间则由迭代算法的77 s缩短为本文算法的14 s，从而使快速4维SPECT定量重建成为可能，可望具有广泛的临床应用前景。

Study on fast and quantitative reconstruction algorithms for dynamic SPECT(4 dimension) under fan beam geometry is conducted. The correlated information along time axis of projection sequences is decorrelated using Karhune Loève (KL) transformation. Then we reconstruct all or part of the components in KL domain with Novikovs inverse formula, which is deduced for fan beam geometry. The results can be obtained by inverse KL transform. The reconstruction can compensate for the nonuniform attenuation effectively. The results are similar to those from iterative approaches while there construction time is greatly abbreviated. The proposed method can reconstruct 4D SPECT fast and quantitatively and thus has a good future in clinical applications.