Aspects of Discrete Tomography

离散断层扫描的各个方面

• 批准号: 0306215
• 负责人: Gabor Herman
• 金额: $ 22.96万
• 依托单位: CUNY Graduate School University Center
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0306215&HistoricalAwards=false
• 关键词: Aspects; Discrete; Tomography

Herman The investigator develops new theoretical results(uniqueness, existence, and complexity theories) in discretetomography), new reconstruction methods (for the case ofabsorption and for label distributions), and applications(neutron tomography). To obtain these results, methods ofdiscrete mathematics, probability theory, and computer scienceare applied, including modeling and simulation studies bycomputers. The new problems that the investigator studies are:(a) discrete tomography with absorption; (b) estimation of theparameters of Gibbs priors to be used in binary tomography; (c)direct recovery of label distributions from projection data; and(d) mathematical problems of reconstruction in neutrontomography. Roughly speaking, tomography deals with the problems ofrecognizing an object from a limited number of views of it, andof discriminating between objects from a limited number of viewsof them. Mathematically, the idea is to reconstruct amultidimensional function that describes, having only a fewlower-dimensional samples -- projections -- of the function.Discrete tomography deals with a special type of tomographicinverse problem in which the function to be reconstructed fromits projections is discrete (i.e., has only a few elements in itsrange of values). In the special case when the function is binary(only two possible values), prior information can be used torecover it from very few (e.g., only 2 or 3) projections.Discrete tomography has some fascinating applications, forexample, in medicine, molecular biology, electron microscopy,security, and nondestructive testing. In this project theinvestigator studies problems in discrete tomography, developsnew methods to reconstruct functions, and considers applicationsin neutron tomography. Other broad impacts include theinvolvement of students in the work of the project, aninternational collaboration with a faculty associate in Hungaryand jointly run research seminar at CUNY, and a workshop on theapplications of discrete tomography.

赫尔曼 研究人员开发新的理论结果（唯一性，存在性和复杂性理论）在离散断层扫描），新的重建方法（吸收和标签分布的情况下），和应用（中子断层扫描）。 为了得到这些结果，离散数学，概率论和计算机科学的方法被应用，包括计算机建模和仿真研究。 研究者研究的新问题是：（a）吸收的离散层析;（B）用于二元层析的Gibbs先验参数的估计;（c）从投影数据直接恢复标记分布;（d）中子层析重建的数学问题。 粗略地说，层析成像处理的问题是从有限的几个视角中识别一个物体，以及从有限的几个视角中区分物体。 从数学上讲，其思想是重建一个多维函数，该函数仅描述函数的几个低维样本-投影。离散断层扫描处理一种特殊类型的断层扫描逆问题，其中要从投影重建的函数是离散的（即，在它的取值范围内只有几个元素）。 在特殊情况下，当函数是二进制的（只有两个可能的值），先验信息可以用来恢复它从很少（例如，离散层析成像在医学、分子生物学、电子显微镜、安全和无损检测等方面有着令人着迷的应用。 在该项目中，研究者研究离散层析成像中的问题，开发新的函数重建方法，并考虑在中子层析成像中的应用。 其他广泛的影响包括学生参与该项目的工作，与匈牙利的一名教员合作并在纽约市立大学联合举办研究研讨会，以及关于离散断层扫描应用的研讨会。