Mathematical Sciences: Radon Transforms and Tomography

昆托将在数学分析中探讨问题， Radon变换和层析成像有两个主要目标。 第一个是证明内射性和支持定理 真实的解析背景下的广义Radon变换 真实的解析子流形上的测度 二是解决 断层扫描中的两个问题。也就是说， 环和火箭出口锥的评估，以及剂量计划 癌症放射治疗的算法。 这个项目中的数学如下。 采取 流形（表面，固体或高维模拟）和 函数。假设流形被分割成 函数在每个切片上的平均值是 知道的 问题是重建原始函数。 一 一个很好的例子是给出每一点密度的函数 指固体内部不能直接进入。 x射线 图像给出了在所述方向上沿着沿着的平均密度。 梁 断层摄影是一门推断物体内部密度的科学， 从这些图像的经济数量的对象。

Quinto will pursue problems in the mathematical analysis of Radon transforms and in tomography with two major objectives. The first is to prove injectivity and support theorems for generalized radon transforms in the setting of real analytic measures on real analytic submanifolds. The second is to solve two problems in tomography. Namely, the non-destructive evaluation of rings and rocket exit cones, and a dose plan algorithm for cancer radiation therapy. The mathematics in this project is as follows. Take a manifold (surface, solid, or higher dimensional analogue) and a function defined on it. Suppose the manifold is sliced up in some fashion and the average of the function over each slice is known. The problem is to reconstruct the original function. A good example is the function that gives the density at each point of a solid body whose inside is not directly accessible . X-ray images give average densities along lines in the direction of the beam. Tomography is the science of deducing densities inside the object from an economical number of these images.