基于Radon变换和滤波反投影算法的CT系统重建算法研究

Study on reconstruction algorithm of CT system based on radon transform and filtered back projection algorithm

图像重建算法是计算机断层成像（CT）技术的核心,而传统的重建算法精度低、复杂度较高。为了优化图像重建算法,本文提出Radon变换算法的一种近似算法,建立CT系统投影优化模型。在研究过程中,为了减少参数,提出分裂降维算法,并采取非线性最小二乘方法,以得到CT系统旋转中心位置。在对几种算法对比中发现,在重建过程中,由于直接反投影法中的均匀回抹思想,得到的CT投影重建图像较模糊,故采用滤波反投影算法。用Shepp-Logan算法对数据滤波,再由滤波后的数据重建出清晰度较高的CT图像。基于数学理论,最后提出精度与稳定性的公式,衡量算法的鲁棒性。实验结果表明,优化后的算法复杂度低、运行速度快,相比于其他图像重建算法成像清晰。

The image reconstruction algorithm is the core of CT technology,while the traditional reconstruction algorithm has low accuracy and high complexity.In order to optimize the image reconstruction algorithm,an approximation algorithm of radon transform algorithm is proposed in this paper,and the projection optimization model of CT system is established.In the research process,a splitting and dimension reduction algorithm is proposed to reduce the parameters,and a nonlinear least squares method is adopted to obtain the rotational center position of the CT system.In the comparison of several algorithms,it is found that during the reconstruction process,the filtered back projection algorithm is adopted because the CT projection reconstruction image is relatively ambiguous due to the uniform erasing idea in the direct back projection method.The Shepp-Logan algorithm was used to filter the data,and the filtered high-resolution CT images were reconstructed from the filtered data.Based on mathematical theory,formulas for accuracy and stability are finally proposed to measure the robustness of the algorithm.The experimental results show that the optimized algorithm is low in complexity and fast in operation,and it is clearer than other image reconstruction algorithms.