Mathematical Sciences: RUI: Geometric Tomography

首席研究员将研究几何层析成像中的问题，并开发从投影重建凸体几何形状的方法。特别是，他将探索从x射线重建凸体和多面体的算法方面的新方向，从x射线中确定它们的相互作用，以及相交体的分类。两名本科生将在首席研究员的指导下完成该项目的部分工作。该奖项将支持积分几何一般领域的研究。一个集合的几何结构通常可以通过将集合分解成片来分析和描述。切片的几何形状通常相当简单，易于描述。分析中的主要困难通常是从切片的几何形状中重建整个集合的底层几何特征。这一数学领域的一个广为人知的应用是CAT扫描。

The principal investigator will study problems in geometric tomography and develop methods to reconstruct the geometry of convex bodies from projections. In particular he will explore new directions in the algorithmic aspects of reconstructing convex bodies and polytopes from X-rays, their interactive determination from X-rays, and the classification of intersection bodies. Two undergraduate students will work on parts of the project under the direction of the principal investigator. This award will support research in the general area of integral geometry. The geometry of a set may often be analyzed and described by a decomposition of the set into slices. The geometry of the slices is often fairly simple and easy to describe. The main difficulty in the analysis is usually the reconstruction of the underlying geometric features of the entire set from the geometry of the slices. One well know application of this area of mathematics is the CAT scan.