Mathematical Sciences: 1993 AMS-SIAM Summer Seminar: The Mathematics of Tomography, Impedance Imaging and Integral Geometry

计算机断层扫描已经从数值分析发展而来， 平面X射线断层扫描仪的算法开发， 涵盖广泛的成像技术。 阻抗成像 系统将电流施加到身体表面，测量感应的 表面上的电压，并从这些信息，重建一个 近似于电导率和/或电 内部的介电常数。 从数学上讲，这个问题是病态的- 提出的和非线性的，和一个经常使用的近似减少到 Radon变换 积分几何是数学基础， 断层扫描和一个用于阻抗成像的模型。 氡 线上变换是X射线层析成像的模型， 一般化模型发射层析成像和问题， 超声. 断层摄影师使用积分几何定理，例如 反演公式和范围特征，以创建和 改进重建方法。 该项目将支持AMS-SIAM夏季研讨会， 层析成像数学中的应用数学，阻抗 成像和积分几何将于1993年6月7日至18日在 位于马萨诸塞州南哈德利的霍利奥克学院。 的特征之一 断层扫描是高水平之间的强关系 数学（如调和分析、偏微分 方程、微局部分析和李群理论）， 应用于医学成像、阻抗成像、放射治疗 工业无损检测。 裁谈会有 以下主要目标：（1）为该领域的研究人员提供 有机会界定和阐明当前的主要问题， （2）确定共同的主题和方法， 加强纯粹和应用方面之间的联系， 这些领域，并促进研究人员之间的对话， 并斩获行业内多项重量级 研究生，最近的博士生，以及 将鼓励该领域的新研究人员参加。

Computed tomography has grown from numerical analysis and algorithm development for planar X-ray tomography scanners to encompass a broad range of imaging techniques. Impedance imaging systems apply current to the surface of a body, measure the induced voltages on the surface, and from this information, reconstruct an approximation to the electrical conductivity and/or electrical permittivity in the interior. Mathematically, the problem is ill- posed and nonlinear, and a frequently used approximation reduces to a Radon transform. Integral geometry is the mathematical basis for tomography and one model for impedance imaging. The Radon transform on lines is the model of X-ray tomography and generalizations model emission tomography and problems in ultrasound. Tomographers use integral geometric theorems, such as inversion formulas and range characterizations, to create and improve reconstruction methods. This project will support the AMS-SIAM Summer Seminar in Applied Mathematics on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry to be held June 7-18, 1993 at Mount Holyoke College in South Hadley, MA. One of the features of tomography is the strong relationship between high level mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and Lie group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial non-destructive evaluation. The conference has the following main goals: (1) to give researchers in the field the opportunity to define and articulate the main problems of current interest and to isolate common themes and approaches and (2) to strengthen the connection between the pure and applied aspects of these areas and to facilitate dialogue between researchers in the various areas. Graduate students, recent doctoral recipients, and new researchers in the field will be encouraged to attend.