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高度 用于计算机 X 射线的可并行、空间、有限角度模型 电子断层扫描，能够真实地进行空间重建 时间。该模型基于氡气的不断扩展 在有限域上的向量空间上进行变换。有限角度 该模型的特点在三维空间中特别重要 使用透射电子显微镜成像，其中倾斜角 限制为 +/-60 度。在设计上也很重要 用于 X 射线断层扫描的扫描设备，因为它允许 消除当前扫描仪的隧道形状。 拟议研究的第一阶段涉及 X 射线断层扫描， 是双重的。首先，根据先前的发现，我们将完成 通过确定产生最小噪声的几何形状进行研究，以及 因此，我们将调整算法来模拟 模型在空间情况下工作，在顺序和并行下 编程。 二是重建与重建质量的比较研究。 速度将被执行，考虑到其他现有的 模型。 第二阶段包括该项目相关的新具体目标 电子断层扫描，即应用我们的修改 使用透射电子显微镜收集的数据的算法， 遵循 P. Schwander（AT&T Bell）最近开发的技术 实验室）以确定晶体的原子结构。施万德的 方法开辟了一个新领域，可以命名为离散二进制 断层扫描，我们的算法似乎运行良好。确实，万一 晶体由一种类型的原子组成，晶体可以被模型化 作为仅由 0 和 1 组成的三维数组 只能测量沿两到四个方向的投影 某些区域轴。因此，启发式在于应用我们的 重建变换为可用的投影，获得 3 维的 值数组。每个值的测量范围为 0.0 到 1.0，给出了该位置存在原子的可能性。 按照这种启发式开发的一些初步算法是 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 数学或计算机专业的少数民族研究生 科学，生物医学研究。 这些至少三年 学生将接受数学方面的个性化培训 断层扫描，将被鼓励攻读生物博士研究 数学，并将负责大部分计算 模型的开发和实施。 该提案的长期目标是创建一个多 纪律环境，涉及少数民族研究生， 数学家、计算机科学家、工程师和物理学家的目标 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。