Reconstruction Algorithm for Computed Tomography

计算机断层扫描(CT)提供了一种非侵入性的方法，可以对物体进行二维、横断面或三维成像。在典型的CT应用中，根据X射线透射率的测量来估计通过物体的衰减系数的分布，并使用该分布来重建物体的图像。目前用于从X射线测量数据生成图像的算法是滤波反投影法(FBP)，该方法在过去30年中一直是主要方法。数学上基于傅里叶变换和卷积的FBP方法是有效的，但它也有一些固有的缺陷。该项目的主要目标是基于一种新的数学方法提供新的算法，这种算法将更有效，产生更高质量的图像，并使用更低的X射线剂量。新算法被称为OpED，因为它基于磁盘上的正交多项式展开。该项目将探索OpEd算法的数学特性，如收敛、速度和分辨率，重点是适用性。它还将研究新算法与X射线输入的扫描几何的兼容性。此外，它的目标是将算法从二维图像扩展到三维图像。brbr计算机断层扫描是生物医学研究的重要工具，已广泛应用于临床和医院的诊断医学。它还在许多其他科学领域得到了广泛的应用，包括物理、化学、天文学、地球物理和生物科学。该项目的目的是为计算机断层成像中的图像重建提供改进的算法。目标是开发算法，在合理的时间内产生高分辨率的图像，几乎没有伪影，并使用相对较低的X射线剂量，以降低过度X射线暴露造成生物损害的风险。这样的算法将使x射线CT在诊断医学中的使用更加有效。

Computed Tomography (CT) offers a non-invasive method for two-dimensional cross-sectional or three-dimensional imaging of an object. In a typical CT application, the distribution of the attenuation coefficient through a body from measurements of x-ray transmission is estimated and used to reconstruct an image of the object. The algorithm currently used to generate an image from x-ray measurement data is the filtered backprojection (FBP) method, which has been the primary method for the past thirty years. The FBP method, based mathematically on the Fourier transform and convolution, is effective, but it also has a number of inherent drawbacks. The main objective of this project is to provide new algorithms, based on a new mathematical approach, that will be more effective, produce images of better quality, and use lower x-ray dose. The new algorithm is called OPED, as it is based on orthogonal polynomial expansions on the disk. The project will explore the mathematical properties of the OPED algorithms, such as convergence, speed, and resolution, with emphasis on applicability. It will also study the compatibility of the new algorithm and the scanning geometry of the x-ray input. Furthermore, it aims at extending the algorithms from two-dimensional to three-dimensional images.brbrComputer tomography is an important tool in biomedical research and has been widely used in diagnostic medicine in clinics and hospitals. It has also found widespread applications in many other scientific fields, including physics, chemistry, astronomy, geophysics, and biological sciences. The purpose of the project is to provide improved algorithms for image reconstruction in computed tomography. The goal is to develop algorithms that will produce images of high resolution with few artifacts in reasonable time and use relatively low x-ray dose to lower the risk of biological damage caused by excessive x-ray exposure. Such an algorithm will make the use of x-ray CT more effective in diagnostic medicine.