Fast Algorithms for Tomography

快速层析成像算法：Yoram BreslerTomography，或从各个方向的线积分集合（称为Radon变换）重建物体是一个研究得很好的问题。 也许最重要的是，它是大多数关键诊断成像模式的基础原理，包括X射线断层扫描（CT），PET和SPECT，某些形式的MRI，以及新兴技术，如电阻抗断层扫描（EIT）和光学断层扫描。 层析成像也是许多其他问题的基本原理和应用在科学和工程-从电子显微镜的亚细胞结构和无损评价（NDE）在制造业，通过地球物理勘探和环境监测，遥感合成孔径雷达（SAR）。 用于解决层析成像问题的最广泛使用的技术被称为滤波反投影（FBP），并且在医学X射线CT领域中无处不在。但是，FBP方法是缓慢的，新技术使数据采集的速度，不能处理的FBP方法和现有的计算机技术成为可能。 这项研究涉及到新的方法来解决断层扫描问题，使用一个非常小的分数所需的努力，由FBP.The调查员正在研究一些有前途的技术，加快FBP重建算法。 他发现Radon变换可以用一种特殊的方式分解，这种新的分解导致了O（N^2 log N）的方法（用于从N个投影重建N X N图像）来解决层析成像问题，而FBP方法是O（N^3）的方法。 对于大的N，如在第三代或第四代X射线CT系统中通常遇到的，这表示接近两个数量级的加速。 这项研究还涉及使用这种分解，以加速解决更复杂的断层扫描问题，其中数据丢失或失真。

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.