Reconstruction Algorithm for Computed Tomography

点击翻译按钮获取中文摘要

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.