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.

断层扫描的快速算法：Yoram Bresler断层扫描，或者从各个方向的线积分集合重建物体（称为氡变换）是一个经过充分研究的问题。 也许最重要的是，它是大多数关键诊断成像模式的基本原理，包括 X 射线断层扫描 (CT)、PET 和 SPECT、某些形式的 MRI 以及电阻抗断层扫描 (EIT) 和光学断层扫描等新兴技术。 断层扫描也是科学和工程中许多其他问题和应用的基本原理——从亚细胞结构的电子显微镜和制造中的无损评估 (NDE)，到地球物理勘探和环境监测，再到合成孔径雷达 (SAR) 遥感。 用于解决断层扫描问题的最广泛使用的技术称为滤波反投影 (FBP)，在医学 X 射线 CT 领域中无处不在。但 FBP 方法速度较慢，而新技术使数据采集成为可能，其速率是 FBP 方法和现有计算机技术无法处理的。 这项研究涉及解决断层扫描问题的新方法，这些方法只需要 FBP 所需工作量的一小部分。研究人员正在研究一些有前途的技术来加速 FBP 重建算法。 他发现 Radon 变换可以用一种特殊的方式进行分解，并且这种新的分解导致了 O(N^2 log N) 方法（用于从 N 个投影重建 N X N 图像）来解决断层摄影问题，而不是到 FBP 方法，这是一个 O(N^3) 方法。 对于第三代或第四代 X 射线 CT 系统中通常遇到的大 N，这代表了近两个数量级的加速。 这项研究还涉及使用这种因式分解来加速解决更复杂的断层摄影问题，其中数据丢失或扭曲。