图像重建模型中基函数的引入

基金项目:

北京市重点建设学科—应用数学PXM2010_014224_096185)

国家自然科学基金项目(60972115)

详细信息

Basis Function Approach to Computerized Tomography

Division of Applied Mathematics, Beijing Information Science & Technology University, Beijing 100101, China

摘要: 基于理想小区域的图像重建离散化模型以理想小区域代替原来传统意义上的像素格,用理想小区域到射线的距离的函数,来衡量射线穿过理想小区域时投影系数的大小。在此图像重建离散化模型中引入基函数。并将离散图像与基函数卷积得到连续的图像,图像中任一点的值可通过选取合适的基函数得到。本文探讨图像重建中基函数需要满足的条件,并分析讨论几种基函数的实例及其频域特性。
- 图像重建 /
- 重建模型 /
- 基函数 /
- 代数迭代
Abstract: We have a image reconstruction of the discrete model that based on the ideal small area replaces the original pixel grid in the traditional sense. The function about the distance form the ideal small area to the ray, to measure the size of the attenuation coefficient when the radiation passes through the ideal small area.In this image reconstruction of the discrete model we introduce the basis function.The discrete image is mapped into continuous image by convolution with a basis function.We discuss the conditions the basis function need to meet and give two basis functions and their firequency properties.
- image reconstruction /
- reconstruction model /
- basis function /
- iterative method