池明辉1，蔡玉芳2*

（1.重庆大学数学与统计学院，重庆401331；2.工业CT无损检测教育部工程研究中心，重庆400044）

*通讯作者Email: aacai@163.com

摘要：针对锥束CT重建FDK算法中系统射线源、转台和探测器平面的几何参数难以准确定位的工程问题，通过理论分析和仿真实验研究了各几何参数误差对重建图像质量的影响。首先，将锥束CT系统的几何参数偏差归结为探测器平面的偏差，通过仿真实验分析了各几何参数偏差对重建图像质量的影响及其伪影特征。实验结果表明：（1）探测器沿中心行或中心列的偏转在偏转角较小时对重建结果影响微小；（2）探测器到射线源和旋转中心距离误差仅影响图像的几何放大倍数；（3）探测器的面内平移和绕探测器中心点旋转会引起环状伪影。最后，推导了含有几种典型几何偏差的FDK图像重建公式，利用该重建公式对存在误差的扫描数据进行重建，消除了几何偏差伪影，显著提高重建图像质量。

关键词：锥束CT；图像重建；FDK；几何校正

Analysis and Calibration of Geometric Parameters in

Cone-Beam CT System

Abstract: Aims to the engineering problem in Cone-Beam CT (Computed To- mography) reconstruction FDK algorithm that the geometric parameters of X-R ay source, turntable and the X-Ray planar detector cannot pinpoint exactly, we give a study of the effect of the geometric parameters of the system on reconstruct image through theoretical analysis and simulation experiment. Firstly, we boil them down to the error of X-Ray planar detector. Besides, we do some experiments to discuss the effects of each of the error on reconstruct image. The results indicate that: (1) the error rotation of the detector around center row or center column has little effects on the reconstruct image if it is enough little; (2) the distance from X-Ray source to the center of planar detector or to center of turntable plays a scaling part of reconstruct image; (3) the translation or rotation of detector in plane would cause serious ring artifacts. At last, we give the expression of the reconstruct formula with some typical error of system geometric parameters. We reconstruct the projection data of a model under the system geometric parameters error with it, the reconstruction results indicate that the proposed method can eliminate the artifacts and improve the quality of CB- CT image.

Keyword: Cone-Beam CT; Image Reconstruction; FDK; Geometric Calibration

1 前言

计算机层析成像技术(Computed Tomography简称CT)是利用射线穿过物体时，不同成分和厚度的物体对射线衰减程度不同的原理来成像。锥束CT的各种重建算法中，FDK算法由于其数学形式简单、计算效率高，且在锥角较小的情况下，能够取得较好的重建效果，因而在实际中有着广泛的应用。