北京生物医学工程

基于投影矩阵广义逆的CT重建迭代算法

Novel iterative algorithm for CT reconstruction based on theMoore-Penrose inverse of projection matrix

作者：王会徐亚楠武王将石宏理杨智罗述谦

单位：首都医科大学生物医学工程学院(北京100069)

分类号：R318.04

出版年·卷·期（页码）：2017·36·3（251-256）

摘要：

目的在CT检查时，有限角度投影和稀疏矩阵投影能够减少X射线的剂量，然而这会导致投影数据不足，给图像重建带来一定的困难。为了克服这一难题得到较好的重建图像，本文提出一种基于计算投影矩阵广义逆的CT迭代重建算法。方法该算法在计算过程中，将重建图像表示为投影矩阵以及其广义逆的乘积。首先使用一阶迭代计算广义逆矩阵，但是由于投影矩阵和其广义逆矩阵都比较大，在迭代过程中以投影和滤波反投影代替。然后通过不同的算法分别对平行束投影、有限角度投影、稀疏矩阵投影的数据进行重建，并对重建结果的均方差、通用图像质量指标以及图像互信息进行比较。结果本文提出的方法重建出图像的均方差、通用图像质量指标和图像互信息更优，而且重建时间较短。结论该方法能够在没有未知图像先验结构信息和伪影猜想的情况下有效地提高重建图像的质量，而且该算法不需要计算投影过程，重建过程简单易行。

Objective In the CT examination, the limited-angle projection and sparse projection methods can be used to reduce the X-ray dose. However, these methods would result in the deficiency of the projection data and bringing certain difficulty for image reconstruction. For the purpose of overcoming the challenges and obtaining a higher quality reconstruction image, a new CT reconstruction method is proposed in this paper. Methods In the proposed method, the reconstruction image was expressed as the multiplication of projection matrix and its the Moose-Penrose pseudo-inverse. The first-order recursive formula was used to calculate the pseudo-inverse. However, the projection matrix and its the Moose-Penrose pseudo-inverse were replaced by projection and filtered back projection in the iterative process because of the difficulty of calculation. Then, the data of the parallel beam projection, the limited-angle projection and the sparse projection were reconstructed by different methods, and the mean square error (MSE), universal quality index (UQI) and mutual information (MI) were used to compare the results of the reconstruction images. Results The results of the MSE, UQI and MI by using the proposed method were better, and the time was less. Conclusions The proposed method can improve the quality of the reconstruction image efficiently without any prior structure information or an artificial assumption on the underlying image. Neither does it need the expression of projection process. The implementation of the proposed method is simple.

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