Fast Algorithms for Tomography

断层扫描快速算法

• 批准号: 9972980
• 负责人: Yoram Bresler
• 金额: $ 19.81万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-15 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9972980&HistoricalAwards=false
• 关键词: Fast; Algorithms; Tomography

FAST ALGORITHMS FOR TOMOGRAPHYPI: Yoram BreslerTomography, or the reconstruction of an object from a collection of its line integrals from various directions (known as its Radon transform) is a well-studied problem. Perhaps most importantly, it is the principle underlying most of the key diagnostic imaging modalities including x-ray Tomography (CT), PET and SPECT, certain forms of MRI, and emerging techniques such as electrical impedance tomography (EIT) and optical tomography. Tomography is also the fundamental principle in numerous other problems and applications in science and engineering -- from electron microscopy of subcellular structures and nondestructive evaluation (NDE) in manufacturing, through geophysical exploration and environmental monitoring, to remote sensing by synthetic aperture radar (SAR). The most widely used technique for solving the tomographic problem is known as Filtered Backprojection (FBP), and is ubiquitous in the realm of medical x-ray CT. But the FBP method is slow, and new technologies are making data acquisition possible at rates that cannot be handled by the FBP method and existing computer technology. This research involves new ways of solving the tomography problem that use a very small fraction of the effort required by the FBP.The investigator is studying a number of promising techniques for accelerating the FBP reconstruction algorithm. He has discovered that the Radon transform can be factored in a special way, and that this new factorization leads to an O(N^2 log N) method (for reconstructing an N X N image from N projections) for solving the tomographic problems, as opposed to the FBP method, which is an O(N^3) method. For large N, as are typically encountered in third or fourth generation x-ray CT systems, this represents a speedup of nearly two orders of magnitude. This research also involves the use of this factorization to accelerate solutions to more complicated tomographic problems, in which data are missing or distorted.

层析成像的快速算法：Yoram Breslertomography，或从各个方向（称为ra tronverally）的线积分集合中重建对象的重建是一个充分的问题。 也许最重要的是，这是大多数关键诊断成像方式的基础，包括X射线层析成像（CT），PET和SPECT，某些形式的MRI以及新兴技术，以及电气阻抗断层扫描（EIT）和光学断层扫描等新兴技术。 层析成像也是科学和工程中许多其他问题和应用中的基本原理 - 从亚细胞结构的电子显微镜以及通过地球物理探索和环境监测到制造业中的非破坏性评估（NDE），再到合成孔径雷达（SAR）的遥感。 解决断层扫描问题的最广泛使用的技术称为过滤后反射（FBP），并且在医疗X射线CT领域无处不在。但是FBP方法很慢，新技术正在以无法通过FBP方法和现有计算机技术来处理的速率使数据获取成为可能。 这项研究涉及解决层析成像问题的新方法，该方法使用FBP所需的很小一部分的努力。研究人员正在研究加速FBP重建算法的许多有希望的技术。 他发现可以以特殊的方式计算ra transform，并且这种新的分解会导致o（n^2 log n）方法（用于从N投影中重建n x n图像）来解决层析成像问题，而不是FBP方法，而FBP方法是O（n^3）方法。 对于大N，正如第三代或第四代X射线CT系统中通常遇到的那样，这代表了将近两个数量级的加速。 这项研究还涉及使用此分解来加速解决方案，以解决更复杂的层析成像问题，其中数据缺失或扭曲。