DEVELOPMENT OF A SPATIAL LIMITED ANGLE MODEL FOR COMPUTERIZED X RAY TOMOGRAPHY

计算机X射线断层摄影空间有限角度模型的开发

• 批准号: 6271553
• 负责人: PABLO SALZBERG
• 金额: $ 10.9万
• 依托单位: UNIVERSITY OF PUERTO RICO RIO PIEDRAS
• 依托单位国家: 美国
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/6271553
• 关键词: bioengineering /biomedical engineering; computed axial tomography; computer simulation; image processing; mathematical model; model design /development

Our research proposal deals with the development of a highly parallelizable, spatial, limited angle model for computerized X-ray and electron tomography, capable to perform spatial reconstructions in real time. This model is based upon a continuous extension of the Radon transform on vector spaces over finite fields. The limited angle feature of this model is specially important in three-dimensional imaging with transmission electron microscopes where the tilting angle is limited to +/-60 degrees. It is also important in the design of scanning devices for X-ray tomography since it.would permit to eliminate the tunnel shape of current scanners. The first phase of the proposed research, regarding X-ray tomography, is two-fold. First, following previous findings, we shall complete the study by determining the geometry that yields minimum noise, and accordingly, we shall adjust the algorithms for simulating how the model works in the spatial case, under sequential and parallel programming. Secondly, a comparative study of the quality of the reconstructions and speed will be performed, taking into consideration other existing models. The second phase consist of a new specific aim of this project related to electron tomography, namely, to apply a modification of our algorithm to data collected by using transmission electron microscopy, following a recent technique developed by P. Schwander (AT&T Bell Labs.) to determine the atomic structure of crystals. Schwander's methods have open a new field which could be named Discrete Binary Tomography, in which our algorithms seem to work well. Indeed, in case that the crystal consists of one type of atom, a crystal can be model as a three dimensional array only of 0's and 1's of which it is possible to measure projection only in two to four directions along certain zone axes. Therefore, the heuristic consists in applying our reconstruction transform to the available projections obtaining a 3-dim array of values. Each of these values, measured on a scale from 0.0 to 1.0, gives the likelihood of the presence of an atom in that position. Some preliminary algorithms developed following this heuristic are yielding promising reconstructions. An important goal of this project is to attract two outstanding graduate minority students majoring in mathematics or in computer sciences, to biomedical research. For at least three years these students will receive personalized training in the mathematics of tomography, will be encouraged to pursue doctoral studies in bio- mathematics, and will be on charge of most of the computational development and implementation of the model. The long-term objectives of this proposal are to create a multi- disciplinary environment, involving graduate minority students, mathematicians, computer scientists, engineers and physicists, aimed at producing biomedical research in the various aspects of tomography, such as a prototype X-ray CT scanner based on our spatial model.

我们的研究计划涉及开发一种高度 用于计算机化X射线的可并行化、空间、有限角度模型， 电子断层摄影术，能够在真实的中进行空间重建 时间这个模型是基于Radon的连续扩展 有限域上向量空间上的变换有限角 这个模型的特点是特别重要的三维 用透射电子显微镜成像， 限制在+/-60度。它在设计中也很重要， 用于X射线断层扫描的扫描装置，因为它允许 消除了当前扫描仪的隧道形状。 拟议研究的第一阶段，关于X射线断层扫描， 是双重的。首先，根据之前的调查结果，我们将完成 通过确定产生最小噪声的几何结构进行研究，以及 因此，我们将调整算法，以模拟 模型适用于空间的情况下，在顺序和并行 编程. 其次，对重建的质量进行了比较研究， 速度将被执行，同时考虑到其他现有的 模型 第二阶段包括一个新的具体目标，该项目有关 电子断层扫描，即，应用我们的修改 算法对通过使用透射电子显微镜收集的数据， 根据P. Schwander（AT&T Bell）开发的最新技术 实验室。）来确定晶体的原子结构施旺德氏 方法开辟了一个新的领域，可以命名为离散二进制 断层扫描，我们的算法似乎工作得很好。事实上，如果 晶体是由一种原子组成的，晶体可以被模拟成 作为一个只有0和1的三维数组， 可以仅在沿沿着的两到四个方向上测量投影 某些区域轴。因此，启发式包括应用我们的 重建变换到可用的投影，获得3维 数组的值。这些值中的每一个，在从0.0到 1.0，给出该位置存在原子的可能性。 一些初步的算法开发后，这种启发式是 产生有希望的重建。 该项目的一个重要目标是吸引两名优秀的 少数民族数学、计算机专业研究生 科学，生物医学研究。 至少三年来， 学生将接受个性化的数学培训， 断层扫描，将被鼓励在生物学博士研究， 数学，并将负责大部分的计算 模型的开发和实施。 该提案的长期目标是建立一个多- 学科环境，包括研究生少数民族学生， 数学家、计算机科学家、工程师和物理学家， 在断层扫描的各个方面进行生物医学研究， 例如基于我们的空间模型的原型X射线CT扫描仪。