对一种非圆轨迹扫描下扇束重建公式的讨论

目的 在CT扇束重建中,源到中心的距离有时需要变化,在这种条件下推导出来的重建公式一般都含有源到中心距离的导数,这不利于公式的实际应用。资料WANG Ge等人在《A Derivative-Free Noncircular Fan-Beam Reconstruction Formula》中提出了一个不含源到中心距离导数的重建公式,并证明在满足三个假设的条件下该公式是一个准确重建公式。但在这个结论的推导过程中存在漏洞,导致这个结论是不成立的。结果 本文指出了这个推导漏洞,对结果重新作了讨论,并且用计算机进行了模拟。结论 得到了很好的效果。

Discuss on a Noncircular Fan-Beam Reconstruction Formula

In fan-beam computed tomography, the source-to-origin distance sometimes varies. In this case, some reconstruction formulae were educed which included the derivative of the source-to-origin distance with respect to the rotation angle, and this feature was not favorable for the practical application. A derivative-free noncircular fan-beam reconstruction formula was brought forward by Ge Wang,,Tein-Hsiang Lin and Ping-chin Cheng. And they proved that the formula was accurate under the condition that the three assumptions were satisfied. But in the course of the deduction, there exists some errors. This paper has pointed out the errors, and made some discusses on the result. Computer simulations give some good results.