【作者】 张銮；

【导师】 桂志国；

【作者基本信息】 中北大学 ， 信号与信息处理， 2010， 硕士

【摘要】 锥束CT在数据采集的速度、空间分辨率以及射线的利用率等方面，明显优于二维平行束和扇束CT，这对医学影像诊断和工业无损检测有着重要的意义。大面积非晶硅平板探测器在工业透射射线成像领域得到越来越多的应用，本文针对平板探测器下采集到的锥束投影数据的特点，系统地研究了三维锥束CT图像重建方法，主要研究内容包括：1.根据笛卡尔坐标与极坐标的转换关系，利用正、余弦函数性质，提出了扇束等距CT极坐标反投影重建快速算法。实验表明该算法的重建速度为传统滤波反投影重建算法的4倍以上，而且不会带来新的重建误差，已成功地将此方法延伸应用到三维锥束重建。2.研究了三维锥束FDK重建算法,分析了其重建特点，并推导了计算机实现的数值化计算方法。根据该算法各重建步骤的特点，提出了FDK优化算法，实验结果表明本文提出的FDK优化算法不但有效地缩短了重建时间，而且其重建质量优越于标准FDK重建算法。3.研究了几种常用的滤波函数，分析了各滤波函数采样序列的特点，在此基础上提出了R-L和Cosine新型混合滤波器，该滤波器结合了R-L和Cosine两种滤波器的优点，在能够保证图像空间分辨率的同时，相对地提高了密度分辨率，对高低频信息作了很好的折衷。实验结果表明该滤波器重建图像误差相对较小，同时具有平滑作用。4.深入研究了一种基于平板探测器的数据重排重建算法——F-FDK算法。该算法借鉴P-FDK算法的思路，并吸收了T-FDK算法的优点，将锥束射线重排为垂直面内为扇形的平行束射线，然后利用平行束重建原理进行重建。该算法对m、n两个方向的投影数据都进行了转换，实现了真正的数据重排。实验结果表明该算法减少了由于锥角增大而导致的伪影，重建图像的效果相对较好。更多还原

【Abstract】 Cone-beam CT outperform 2D parallel-beam and fan-beam CT in the aspects ofacquisition data speed, spatial resolution and ray utilization rate, which are very significant formedical diagnosis and industrial non-destructive testing. Large-areas amorphous siliconflat-panel detector becomes more and more popular in the field of industry ray imaging. Inthis paper, 3D cone-beam CT image reconstruction method is researched systematically,according to the characteristics of the cone-beam projection data based on the flat-paneldetector. The main contents of the paper include the following:According to the transformation relationship between Cartesian coordinates and polarcoordinates, this paper proposes a fast reconstruction algorithm for the back-projectionalgorithm of the polar coordinates for fan-beam collinear equispaced CT based on the featuresof sine and cosine function. The experimental results show that, compared with the traditionalfiltered back-projection algorithm, this method can improve the reconstruction speed by morethan 4 times, and will not bring new reconstruction error. This method has been successfullyapplied to the reconstruction of 3D cone-beam.The 3D cone-beam FDK reconstruction algorithm is discussed and the characteristics ofthis algorithm are analyzed. The numerical calculation method of the computer realization isalso derived in this paper. Moreover, the FDK optimization algorithm is proposed accordingto the characteristics of the reconstruction steps. The experimental results show that theproposed optimization algorithm can effectively shorten the reconstruction time and it issuperior to the standard FDK reconstruction algorithm in the reconstruction image quality.On the basis of discussing several common filter functions and analyzing thecharacteristics of the sample sequence for each filter function, a mixed filter functioncombining with the R-L and Cosine filer function is proposed in this paper. And the proposed filter integrates with the advantages of R-L and Cosine filter function. While this filter canguarantee the image spatial resolution, it relatively increases the density. This filter makes agood compromise between the high and low frequency information. The experimental resultsshow that the error of the reconstructed image by the proposed filter is relatively small. At thesame time, it smoothed the image.This paper also focuses on the study of the projection data rebinning algorithm namedF-FDK based on flat panel detector. This algorithm which refers to the idea of P-PDKalgorithm and absorbs the advantages of T-FDK algorithm, rearranges the cone-beam datainto fan-beam data in the vertical plane, then reconstructs image by the principle of theparallel-beam. This algorithm truly achieves the data rebinning by converting projection datain both directions of m and n. The experimental results show that F-FDK algorithm reducedthe artifact which caused by the cone angle increasing, and the reconstruction image qualitycan be obviously improved.更多还原