中文摘要：

由于扇形束CT图像重建易于实现和控制,被广泛应用于医学和工业无损检测.为了解决截断投影数据的精确重建问题,该算法提出一种基于PI线的扇形束反投影滤波（backprojection filtration,BPF）局部重建算法,先将获得的投影数据微分,再将微分的数据加权反投影到平行的PI线上,最后沿PI线方向进行有限Hilbert变换获得重建图像.该算法只利用理论上最少的投影数据就实现了图像的精确全局重建,同时利用求导和有限Hilbert变换的局部特性最终实现了图像的精确局部重建,减少了成像扫描和对被扫描物体的辐射剂量;最后还利用不同的求导方法和插值方法进行仿真,比较其对重建图像的影响,三点求导和线性插值能使图像获得更高的精度,伪影较少,更具利用价值.

英文摘要：

Due to the fan-beam CT image reconstruction easy to implement and control, it is widely used in medicine and industrial non-destructive testing. In order to solve the problem of truncation accurate reconstruction of projection data, this algorithm proposes a fan-beam of backprojection filtration （BPF） local reconstruction algorithm based on PI-line, it first to differential obtained projection data, then the differential data weighted against projected onto a set of parallel PI-lines, finally it acquires reconstruction image through the limited Hilbert transform along PI-line direction. This algorithm only use the least theoretically projection data of truncated projec- tion data can realize the precise global reconstruction of the image, at the same time the local features of derivation and limited the Hilbert transform finally achieved accurate local reconstruction, it can reduce the imaging scans and irradiation dose of the scanned ob- ject;At last,by using different derivation method and interpolation method through simulation experiments to compare their influence on reconstruction image, it shows that three derivative and linear interpolation can get higher accuracy, and the image artifact is less. So it has more use value.