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

我们的研究方案涉及开发一种简单、快速、高度 用于计算机X射线层析成像的可并行和有限角度模型， 能够实时执行空间重建。启发式算法 这种模式是由P.I.通过几份出版物介绍的，其中包括 学生们。 在研究的第一阶段，我们将完成研究和 同时，开发模拟模型工作方式的算法 在平面情况下。其次，比较研究了教育质量问题。 将执行重建和速度，考虑到 其他现有型号。由于所提出的模型所依据的理论 允许它扩展到三维或更多维度，即 拟议的研究将致力于开发空间的算法 模型，并执行类似于为 第二阶段。 这个项目的一个重要目标是吸引两名优秀的学生， 本科生1名，数学或计算机专业 科学，到生物医学研究。三年来，这些学生将 接受个性化培训，重点是数学或 将鼓励体层摄影术在生物医学领域攻读博士学位 数学，并将负责大部分计算开发 并对该模型进行了实现。 这项提议的长期目标是创建一个多学科的 环境，涉及本科生和研究生、数学家、 计算机科学家、工程师和物理学家，旨在生产原型 基于空间模型的CT扫描仪表现出较高的性能 在第二和第三阶段进行测试的。

Our research proposal deals with the development of a simple, fast, highly parallelizable, and limited angle model for computerized X-ray tomography, capable to perform spatial reconstructions in real time. The heuristic for the model has been introduced by the P.I. through several publications with students. In the first phase of our research, we shall complete the study and simultaneously, develop the algorithms for simulating how the model works in the planar case. Secondly, a comparative study of the quality of the reconstructions and speed will be performed, taking into consideration other existing models. Since the theory subjacent to the proposed model allows it extension to three or more dimensions, the third phase of the proposed research will be devoted to develop the algorithms for a spatial model and to perform a comparative study similar to that described for the second stage. An important goal of this project is to attract 2 outstanding students, graduate and 1 undergraduate, majoring in mathematics or in computer sciences, to biomedical research. For three years, these students will receive personalized training with emphasis on the mathematics or 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 objective of this proposal is to create a multi-disciplinary environment, involving undergraduate and graduate students, mathematicians, computer scientists, engineers and physicists, aimed at producing prototype CT scanner based on the spatial model showing higher performance among those tested in the second and third stages.