Mathematical Sciences: RUI: Geometric Tomography

提出的研究是在几何层析成像和凸性理论领域。提议者希望扩展他早期关于处理凸体的Busemann-Petty问题的工作：Busemann-Petty问题涉及从关于两个凸体中心截面的信息中得出关于n空间中两个凸体相对体积的结论。考虑了用少量x射线图像重建凸体的x射线问题；拟议的研究在计算机断层扫描（CAT和MRI扫描仪）中具有潜在的重大影响。

Gardner 9501289 The proposed research is in the area of geometric tomography and convexity theory. The proposer wishes to extend his earlier work on the Busemann-Petty problem dealing with convex bodies: the Busemann-Petty problem has to do with drawing conclusions about the relative volumes of two convex bodies in n-space from information about their central sections. The X-ray problem - reconstruction of a convex body from a small number of X-ray pictures - is considered; the proposed research has potentially significant ramifications in computerized tomography (CAT and MRI scanners).