南方医科大学学报 ›› 2024, Vol. 44 ›› Issue (4): 682-688.doi: 10.12122/j.issn.1673-4254.2024.04.09

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基于高维PDE投影恢复的低剂量CT重建方法

牛善洲,唐诗洲,黄舒彦,梁礼境,李 硕,刘汉明   

  1. 赣南师范大学数学与计算机科学学院,赣州市计算成像重点实验室,江西 赣州 341000
  • 发布日期:2024-04-29

Low-dose CT reconstruction based on high-dimensional partial differential equation projection recovery

NIU Shanzhou, TANG Shizhou, HUANG Shuyan, LIANG Lijing, LI Shuo, LIU Hanming   

  1. School of Mathematics and Computer Science, Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
  • Published:2024-04-29

摘要: 目的 提出一种基于高维偏微分方程(PDE)投影恢复的低剂量CT重建方法。方法 先将原始的投影数据映射到高维空间中,构造投影数据的高维表示,通过移动高维空间中的点来对高维表示进行更新,再使用偏微分方程对投影数据进行滤波,最后将恢复后的数据使用FBP算法重建出最终CT图像。结果 在Shepp-Logan体模实验中,与FBP,PWLS-QM和TGV-WLS方法相比,新方法在相对均方根误差指标上分别降低了68.87%、50.15%和27.36%,结构相似性上分别提高了23.50%,8.83%和1.62%,特征相似性上分别提高了17.30%、2.71%和2.82%。在腹部临床数据实验中,与FBP,PWLS-QM和TGV-WLS方法相比,新方法在相对均方根误差中分别降低了42.09%、31.04%和21.93%,结构相似性上分别提高了18.33%、13.45%和4.63%,特征相似性上分别提高了3.13%、1.46%和1.10%。结论 本研究提出的新方法在有效去除低剂量CT图像中的条形伪影和噪声的同时,可以保持图像的空间分辨率。

关键词: 低剂量CT;偏微分方程;投影数据恢复;图像重建

Abstract: Objective We propose a low-dose CT reconstruction method using partial differential equation (PDE) denoising under high-dimensional constraints. Methods The projection data were mapped into a high-dimensional space to construct a high-dimensional representation of the data, which were updated by moving the points in the high-dimensional space. The data were denoised using partial differential equations and the CT image was reconstructed using the FBP algorithm. Results Compared with those by FBP, PWLS-QM and TGV-WLS methods, the relative root mean square error of the Shepp-Logan image reconstructed by the proposed method were reduced by 68.87% , 50.15% and 27.36% , the structural similarity values were increased by 23.50%, 8.83% and 1.62%, and the feature similarity values were increased by 17.30%, 2.71% and 2.82%, respectively. For clinical image reconstruction, the proposed method, as compared with FBP, PWLS-QM and TGV-WLS methods, resulted in reduction of the relative root mean square error by 42.09%, 31.04% and 21.93%, increased the structural similarity values by 18.33% , 13.45% and 4.63% , and increased the feature similarity values by 3.13% , 1.46% and 1.10%, respectively. Conclusion The new method can effectively reduce the streak artifacts and noises while maintaining the spatial resolution in reconstructed low-dose CT images.

Key words: low-dose CT; partial differential equations; projection restoration; image reconstruction