扇形束投影用于单光子发射型CT中可以较大地提高系统的灵敏度，却带来投影数据截断产生的伪影问题。多聚焦格式采集投影数据是近几年提出的，它可以避免扇形束投影截断问题。针对多聚集投影数据的重建，此文提出了一种新的基于Fourier级数展开和正则化技巧的近似级数展开算法。该方法推导简单严格。它可应用于平行束和扇形束的重建。新算法在实时可采用快速璃散Fourier算法和不等距的梯形求积公式。数值实验表明该方

Image reconstruction is one of the most exciting borderline science in the last few decades. Many applications have become known such as in diagnostic radiology, nuclear medicine, industry checking and etc. We know that fan-beam projection is a widely used scheme in these applications. One disadvantage of fan-beam projection is the truncation problem in some case which results in ring artifacts in the reconstruction. To resolve this problem, multi focal fan-beam projection is proposed in recent years to avoid the truncation problem and at the same time in the fan-beam projection' s good sensitivity especially for imaging of small organs is maintained. But the famous filering back projection method which is quick and efficient, can not be extended to such projection. In this thesis we advance a new method based on expanding fourier series and regularization technique. The method is as simple as the famous filtering back projection method and its simplified form can be applied to parallel-beam and fan-Beam cases. In implementing it, FFT is used to reduce the time of computation. Through computer simulation, it is found that the new method is noise-insensitivity and can produce accurate reconstruction almost without any visible artifacts when intensifying projection.