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

我们的研究计划涉及开发一种简单，快速，高度 可并行化和有限角度的计算机X射线断层扫描模型， 能够执行真实的时间空间重建。 启发式的 这个模型是由私家侦探通过几个出版物， 学生 在研究的第一阶段，我们会完成研究， 同时，开发用于模拟模型如何工作的算法 在平面的情况下。 第二，比较研究 重建和速度将被执行，考虑到 现有的其他模型。 由于该理论服从于所提出的模型， 允许它扩展到三个或更多的维度，第三阶段的 拟议的研究将致力于开发空间的算法 模型，并进行类似于所述的比较研究， 第二阶段。 本项目的一个重要目标是吸引2名优秀学生， 研究生和1名本科生，主修数学或计算机 科学，生物医学研究。 三年来，这些学生将 接受个性化的培训，重点是数学或 断层扫描将被鼓励追求生物博士研究， 数学，并将负责大部分的计算开发 以及模型的实施。 这项建议的长期目标是建立一个多学科的 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扫描仪显示出更高的性能， 在第二和第三阶段测试的那些。

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.