体积CT精确重建的完全性条件研究

Study on the Complete Conditions for Exact Reconstruction in Volume CT

体积 CT同断层 CT相比有着显著的优越性 ,因而体积 CT将逐渐取代现在广泛使用的断层 CT。我们提出了圆加垂直弧段及三棱锥的三棱线这两种新的锥顶轨迹 ,并研究了以其进行精确重建所需的完全性条件。我们还给出了圆加单条和双条直线及垂直双圆的锥顶轨迹的完全性条件的一种新的证明方法 ,并得出了正确的结论。最后将所得结论推广到了圆加多条直线的情形。

Computed Tomography(CT) is one of the successful methods, in which mathematical theories are combined with engineering technology. Volume CT will replace the cross sectional CT that has been widely used. In this paper two new cone vertex orbits, which are circle and arc and regular triangular pyramid lines, have been proposed and their complete conditions for exact reconstruction have been obtained. After having studied circle and n line cone vertex orbit which is one of the important orbits in volume CT, we have given a better proof about the complete condition in circle and line and circle and 2 line cone vertex orbit and have obtained some proper conclusions. Finally, we extend the above results to circle and n line vertex orbit. These results will be useful for the design of direct volume imaging.