搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于CT扫描数据的X射线能谱估计方法

陈鑫洁 张敬娜 张慧滔 夏迪梦 徐文峰 朱溢佞 赵星

引用本文:
Citation:

基于CT扫描数据的X射线能谱估计方法

陈鑫洁, 张敬娜, 张慧滔, 夏迪梦, 徐文峰, 朱溢佞, 赵星

Computed tomography data based X-ray spectrum estimation method

Chen Xin-Jie, Zhang Jing-Na, Zhang Hui-Tao, Xia Di-Meng, Xu Wen-Feng, Zhu Yi-Ning, Zhao Xing
PDF
HTML
导出引用
  • X射线能谱在计算机层析成像(computed tomography, CT)图像硬化校正、双能谱CT成像、辐射剂量计算等方面具有重要作用. 常用的估计X射线能谱分布的方法, 利用X射线穿过不同厚度模体的衰减数据, 来间接估计X射线能谱分布. 由于该问题具有严重的病态性, 因此如何鲁棒和准确地求解是能谱估计问题的关键. 本文提出了一种利用CT扫描数据来估计X射线能谱分布的方法. 该方法中考虑了谱估计和图像重建之间的相互印证关系, 即谱估计正确时重建的CT图像无硬化伪影, 而重建图像无硬化伪影时, 则说明估计的谱准确. 该方法利用这种相互印证关系构造优化模型, 通过交替迭代求解, 估计能谱分布和重建无硬化伪影的CT图像. 数值实验和实际实验结果表明, 该方法可以准确、鲁棒地估计出 X 射线能谱.
    X-ray spectrum plays an important role in computed tomography (CT) beam hardening correction, dual spectral X-ray CT imaging, and radiation dose calculation. The commonly used method to estimate X-ray spectrum is to estimate the spectra indirectly by using the attenuation data of X-ray passing through the phantoms with different thickness. Since the problem is seriously ill-conditioned, how to choose a suitable mold, establish scanning models and construct solving methods to improve the robustness and accuracy of energy spectrum estimation is the focus of this paper. In this work, in the absence scattering, we present a method to estimate the distribution of the X-ray spectrum by using CT scanning data. In this method, the mutual verification relationship between spectral estimation and image reconstruction is considered. That is, when the spectral estimation is correct, the spectral information can be used to construct a correction algorithm to remove hardening artifacts, and the image without hardening artifacts can be obtained. When the reconstructed image has no hardening artifact, it can indirectly prove that the estimated spectrum is accurate. For single-material molds, when there is no hardening artifact, CT images are fragmentation constant, which can be described by image total variation (TV) minimum. In this method, the mutual corroboration relationship is used to construct an optimization model, and then the X-ray spectrum is estimated and CT images without hardening artifacts are reconstructed through alternate iterative solutions. The characteristic of this method is that it does not necessitate obtaining the cross-line length of the measured mold with different thickness in advance, and it does not require high production precision of the said mold either. When there is a small amount of scattering in CT scanning data, the proposed method can also better estimate the energy spectrum, except for the large deviation in the high-energy part. However, as the scattering ratio increases, the high-energy portion of the energy spectrum will increase, resulting in the estimated spectrum differing greatly from the actual spectrum. Therefore, in the actual experiment, we add collimors in front of the X-ray source and detector to reduce the influence of scattering on the energy spectrum estimation. The numerical result and experimental result show that the proposed method can accurately and robustly estimate the X-ray energy spectrum.
      通信作者: 张慧滔, zhanght@cnu.edu.cn
    • 基金项目: 国家重点研发计划 (批准号: 2022YFF0607800) 和国家自然科学基金 (批准号: 61971293, 61827809, 61671311) 资助的课题.
      Corresponding author: Zhang Hui-Tao, zhanght@cnu.edu.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFF0607800) and the National Natural Science Foundation of China (Grant Nos. 61971293, 61827809, 61671311).
    [1]

    Jarry G, Demarco J J, Beifuss U, Cagnon C H, Mcnitt-Gray M F 2003 Phys. Med. Biol 48 2645Google Scholar

    [2]

    Zhao Y S, Zhao X, Zhang P 2015 IEEE Trans. Med. Imaging 34 761Google Scholar

    [3]

    Elbakri, Idris A, Jeffrey A, Fessler 2002 IEEE Trans. Med. Imaging 21 89Google Scholar

    [4]

    张慧滔, 张朋 2013 光学学报 33 8Google Scholar

    Zhang H T, Zhang P 2013 Acta Opt. Sin. 33 8Google Scholar

    [5]

    Francois P, Catala A, Scouarnec C 1993 Med. Phys. 20 1695Google Scholar

    [6]

    Tominaga, Shoji 1986 Nucl Instrum. Methods Phys. Res. 243 530Google Scholar

    [7]

    Armbruster B, Hamilton R J, Kuehl A K 2004 Phys. Med. Biol 49 5087Google Scholar

    [8]

    Leinweber C, Maier J, Kachelrie M 2017 Med. Phys. 44 6183Google Scholar

    [9]

    Duan X, Wang J, Yu L, Leng S, McCollough C H 2011 Med. Phys. 38 993Google Scholar

    [10]

    罗婷, 李孟飞, 赵云松 2018 电子学报 46 8Google Scholar

    Luo T, Li M F, Zhao Y S 2018 Acta Electron. Sin. 46 8Google Scholar

    [11]

    Sidky E Y, Yu L, Pan X, Zou Y, Vannier M 2005 J. Appl. Phys. 97 623Google Scholar

    [12]

    Zhang L, Zhang G, Chen Z, Xing Y, Cheng J, Xiao Y 2007 IEEE Nuclear Science Symposium Conference Record Honolulu, HI, October 26—November 3, 2007 p3089

    [13]

    杨莹, 牟轩沁, 余厚军, 陈希, 张砚博, 汤少杰 2010 电子学报 38 7Google Scholar

    Yang Y, Mou X Q, Yu H J, Chen X, Zhang Y B, Tang S J 2010 Acta Electron. Sin. 38 7Google Scholar

    [14]

    Perkhounkov B, Stec J, Sidky E Y, Pan X C 2016 Spie Medical Imaging San Diego, America, February 27–March 3, 2016 p1315

    [15]

    Zhao W, Niu K, Schafer S, Royalty K 2014 Phys. Med. Biol 60 339Google Scholar

    [16]

    Zhao W, Xing L, Zhang Q, Xie Q, Niu T 2017 J. Med. Imaging 4 023506Google Scholar

    [17]

    Tucker D M, Barnes G T, Chakraborty D P 1991 Med. Phys. 18 211Google Scholar

    [18]

    Hernandez A M, Boone J M 2014 Med. Phys. 41 042101Google Scholar

    [19]

    Herman G T, Meyer L B 1993 IEEE Trans. Med. Imaging 12 600Google Scholar

    [20]

    Goldstein T, Osher S 2009 SIAM J. Imaging Sci. 2 323Google Scholar

    [21]

    Zhang H M, Wang L Y, Yan B, Li L, Xi X Q, Lu L Z 2013 Chin. Phys. B 22 078701Google Scholar

    [22]

    黄力宇, 朱守平, 匡涛 2015 医学断层图像重建仿真实验 (西安: 西安电子科技大学出版社) 第138—145页

    Huang L Y, Zhu S P, Kuang T 2015 Simulation Experiment of Medical Image Reconstruction (Xi’an: Xidian University Press) pp138–145 (in Chinese)

    [23]

    Sun M, Star-Lack J M 2010 Phys. Med. Biol. 55 6695Google Scholar

  • 图 1  80 kV下X射线能谱估计及重建结果 (a) 无噪声条件下能谱估计结果; (b) 泊松噪声条件下能谱估计结果; (c) NRMSE随迭代次数的变化曲线; (d) 无噪声条件下ART重建结果; (e) 无噪声条件下本文方法重建图; (f) 图(d)和(e)中心行剖线对比图; (g) 有噪声条件下ART重建结果; (h) 有噪声条件下本文方法重建图; (i) 图(g)和(h)中心行剖线对比图

    Fig. 1.  X-ray energy spectrum estimation and reconstruction results at 80 kV: (a) Results of X-ray spectrum estimation without noise; (b) X-ray spectrum estimation results under Poisson noise condition; (c) curve of NRMSE with the number of iterations; (d) ART reconstruction results in noise-free condition; (e) reconstruction image of the proposed method under noise-free condition; (f) Figs. (d) and (e) comparison of section lines in the center row; (g) ART reconstruction results in noisy conditions; (h) reconstruction image of the proposed method under noisy condition; (i) Figs. (g) and (h) comparison of section lines in the center row.

    图 2  散射条件下的实验结果 (a) 散射占比为1%时的能谱估计图; (b) 散射占比为5%时的能谱估计图

    Fig. 2.  Experimental results under scattering conditions: (a) Energy spectrum estimation for 1% scattering; (b) energy spectrum estimation for 5% scattering.

    图 3  不同电压下X射线能谱估计及重建结果 (a) 140 kV下能谱估计结果; (b) 125 kV下能谱估计结果; (c) 60 kV下能谱估计结果; (d) 140 kV下本文方法重建图; (e) 125 kV下本文方法重建图; (f) 60 kV下本文方法重建图; (g) 140 kV下本文方法重建图和ART重建图中心行剖线对比图; (h) 125 kV下本文方法重建图和ART重建图中心行剖线对比图; (i) 60 kV下本文方法重建图和ART重建图中心行剖线对比图

    Fig. 3.  X-ray energy spectrum estimation and reconstruction results under different voltages: (a) X-ray spectrum estimation at 140 kV; (b) X-ray spectrum estimation at 125 kV; (c) X-ray spectrum estimation at 60 kV; (d) reconstruction image of the proposed method at 140 kV; (e) reconstruction image of the proposed method at125 kV; (f) reconstruction image of the proposed method at 60 kV; (g) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART at 140 kV; (h) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART at 125 kV; (i) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART at 60 kV.

    图 4  不规则模体图 (a) 模体a是在实验1的圆铝的基础上内部掏空了两个直径为10 mm的小圆; (b) 模体b是一个不规则的单材质铝材料模体

    Fig. 4.  Irregular phantom diagram: (a) Phantom a was hollowed out with two small circles of 10 mm on the basis of the round aluminum in experiment 1; (b) phantom b is an irregular, single-material aluminum phantom.

    图 5  模体a实验结果图 (a) 能谱估计结果; (b) 本文方法重建图; (c) 本文方法重建图和ART重建图中心行剖线对比图

    Fig. 5.  Experimental results of phantom a: (a) Results of X-ray spectrum estimation; (b) reconstruction image of the proposed method; (c) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART.

    图 6  模体b实验结果图 (a) 能谱估计结果; (b) 本文方法重建图; (c) 本文方法重建图和ART重建图中心行剖线对比图; (d) 真实投影图; (e) 估计投影图; (f) 同一个扫描角度下真实投影数据和估计投影数据对比图

    Fig. 6.  Experimental results of phantom b: (a) Results of X-ray spectrum estimation; (b) reconstruction image of the proposed method ; (c) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART; (d) real projection diagram; (e) estimated projection diagram; (f) comparison of real and estimated projected data at one angle.

    图 7  铜材质谱估计及重建结果图 (a) 能谱估计结果; (b) 本文方法重建图; (c) 本文方法重建图和ART重建图中心行剖线对比图

    Fig. 7.  Spectrum estimation and reconstruction results of copper: (a) Results of X-ray spectrum estimation; (b) reconstruction image of the proposed method; (c) comparison of section lines in the center of the reconstructed image with the proposed method and the reconstructed image with ART.

    图 8  实采CT系统示意图 (a) 实采CT扫描系统; (b) 模体图

    Fig. 8.  Schematic diagram of real CT system: (a) Real CT scanning system; (b) phantom.

    图 9  实际CT系统的实验结果 (a) 能谱估计图; (b) ART重建图; (c) 本文方法重建图; (d) 图(b)和(c)中心行的剖线对比图; (e) 一个角度下真实投影数据和估计投影数据的对比图

    Fig. 9.  Experimental results of a real CT system: (a) X-ray spectrum estimation; (b) ART reconstruction image; (c) reconstruction image of the proposed method; (d) Figs. (b) and (c) comparison of section lines in the center row; (e) comparison of real and estimated projected data at one angle.

    表 1  模拟CT扫描系统的实验参数

    Table 1.  Experimental parameters of simulated CT scanning system.

    参数名称
    射线源到探测器的距离/mm1080
    射线源到旋转中心的距离/mm 589.3525
    扫描角度/(°) $ 360 $
    扫描角度个数 $ 720 $
    探测器单元大小/mm 0.278
    探测器个数 $ 1136 $
    下载: 导出CSV

    表 2  实际CT扫描系统的实验参数

    Table 2.  Experimental parameters of real CT scanning system.

    参数名称
    射线源到探测器的距离/mm 634
    射线源到旋转中心的距离/mm 239
    扫描角度/(°) $ 360 $
    扫描角度个数 $ 720 $
    探测器单元大小/mm 0.2
    探测器个数 $2048×2048$
    下载: 导出CSV
  • [1]

    Jarry G, Demarco J J, Beifuss U, Cagnon C H, Mcnitt-Gray M F 2003 Phys. Med. Biol 48 2645Google Scholar

    [2]

    Zhao Y S, Zhao X, Zhang P 2015 IEEE Trans. Med. Imaging 34 761Google Scholar

    [3]

    Elbakri, Idris A, Jeffrey A, Fessler 2002 IEEE Trans. Med. Imaging 21 89Google Scholar

    [4]

    张慧滔, 张朋 2013 光学学报 33 8Google Scholar

    Zhang H T, Zhang P 2013 Acta Opt. Sin. 33 8Google Scholar

    [5]

    Francois P, Catala A, Scouarnec C 1993 Med. Phys. 20 1695Google Scholar

    [6]

    Tominaga, Shoji 1986 Nucl Instrum. Methods Phys. Res. 243 530Google Scholar

    [7]

    Armbruster B, Hamilton R J, Kuehl A K 2004 Phys. Med. Biol 49 5087Google Scholar

    [8]

    Leinweber C, Maier J, Kachelrie M 2017 Med. Phys. 44 6183Google Scholar

    [9]

    Duan X, Wang J, Yu L, Leng S, McCollough C H 2011 Med. Phys. 38 993Google Scholar

    [10]

    罗婷, 李孟飞, 赵云松 2018 电子学报 46 8Google Scholar

    Luo T, Li M F, Zhao Y S 2018 Acta Electron. Sin. 46 8Google Scholar

    [11]

    Sidky E Y, Yu L, Pan X, Zou Y, Vannier M 2005 J. Appl. Phys. 97 623Google Scholar

    [12]

    Zhang L, Zhang G, Chen Z, Xing Y, Cheng J, Xiao Y 2007 IEEE Nuclear Science Symposium Conference Record Honolulu, HI, October 26—November 3, 2007 p3089

    [13]

    杨莹, 牟轩沁, 余厚军, 陈希, 张砚博, 汤少杰 2010 电子学报 38 7Google Scholar

    Yang Y, Mou X Q, Yu H J, Chen X, Zhang Y B, Tang S J 2010 Acta Electron. Sin. 38 7Google Scholar

    [14]

    Perkhounkov B, Stec J, Sidky E Y, Pan X C 2016 Spie Medical Imaging San Diego, America, February 27–March 3, 2016 p1315

    [15]

    Zhao W, Niu K, Schafer S, Royalty K 2014 Phys. Med. Biol 60 339Google Scholar

    [16]

    Zhao W, Xing L, Zhang Q, Xie Q, Niu T 2017 J. Med. Imaging 4 023506Google Scholar

    [17]

    Tucker D M, Barnes G T, Chakraborty D P 1991 Med. Phys. 18 211Google Scholar

    [18]

    Hernandez A M, Boone J M 2014 Med. Phys. 41 042101Google Scholar

    [19]

    Herman G T, Meyer L B 1993 IEEE Trans. Med. Imaging 12 600Google Scholar

    [20]

    Goldstein T, Osher S 2009 SIAM J. Imaging Sci. 2 323Google Scholar

    [21]

    Zhang H M, Wang L Y, Yan B, Li L, Xi X Q, Lu L Z 2013 Chin. Phys. B 22 078701Google Scholar

    [22]

    黄力宇, 朱守平, 匡涛 2015 医学断层图像重建仿真实验 (西安: 西安电子科技大学出版社) 第138—145页

    Huang L Y, Zhu S P, Kuang T 2015 Simulation Experiment of Medical Image Reconstruction (Xi’an: Xidian University Press) pp138–145 (in Chinese)

    [23]

    Sun M, Star-Lack J M 2010 Phys. Med. Biol. 55 6695Google Scholar

  • [1] 张海鹏, 赵昌哲, 鞠晓璐, 汤杰, 肖体乔. 基于迭代重构算法改进晶体衍射分光X射线鬼成像的图像质量研究. 物理学报, 2022, 71(7): 074201. doi: 10.7498/aps.71.20211978
    [2] 周腊珍, 夏文静, 许倩倩, 陈赞, 李坊佐, 刘志国, 孙天希. 一种基于毛细管X光透镜的微型锥束CT扫描仪. 物理学报, 2022, 71(9): 090701. doi: 10.7498/aps.71.20212195
    [3] 张芝振, 李亮. X射线荧光CT成像中荧光产额、退激时间、散射、偏振等关键物理问题计算与分析. 物理学报, 2021, 70(19): 195201. doi: 10.7498/aps.70.20210765
    [4] 王一诺, 宋昭阳, 马玉林, 华南, 马鸿洋. 基于DNA编码与交替量子随机行走的彩色图像加密算法. 物理学报, 2021, 70(23): 230302. doi: 10.7498/aps.70.20211255
    [5] 苏博, 陶芬, 李可, 杜国浩, 张玲, 李中亮, 邓彪, 谢红兰, 肖体乔. 同步辐射纳米CT图像配准方法研究. 物理学报, 2021, 70(16): 160704. doi: 10.7498/aps.70.20210156
    [6] 乔志伟. 总变差约束的数据分离最小图像重建模型及其Chambolle-Pock求解算法. 物理学报, 2018, 67(19): 198701. doi: 10.7498/aps.67.20180839
    [7] 戚俊成, 陈荣昌, 刘宾, 陈平, 杜国浩, 肖体乔. 基于迭代重建算法的X射线光栅相位CT成像. 物理学报, 2017, 66(5): 054202. doi: 10.7498/aps.66.054202
    [8] 韩玉, 李磊, 闫镔, 席晓琦, 胡国恩. 一种基于Radon逆变换的半覆盖螺旋锥束CT重建算法. 物理学报, 2015, 64(5): 058704. doi: 10.7498/aps.64.058704
    [9] 陈平, 阴晓刚, 潘晋孝, 韩焱. 递变能量X射线高动态融合图像的灰度表征算法研究. 物理学报, 2014, 63(20): 208703. doi: 10.7498/aps.63.208703
    [10] 毛宝林, 陈晓朝, 孝大宇, 范晟昱, 滕月阳, 康雁. 基于全变分最小化和快速一阶方法的低剂量CT有序子集图像重建. 物理学报, 2014, 63(13): 138701. doi: 10.7498/aps.63.138701
    [11] 魏星, 闫镔, 张峰, 李永丽, 席晓琦, 李磊. 多金属物体CT图像的金属伪影校正. 物理学报, 2014, 63(5): 058702. doi: 10.7498/aps.63.058702
    [12] 杨富强, 张定华, 黄魁东, 王鹍, 徐哲. CT不完全投影数据重建算法综述. 物理学报, 2014, 63(5): 058701. doi: 10.7498/aps.63.058701
    [13] 徐宁, 陈雪莲, 杨庚. 基于改进后多维数据加密系统的多图像光学加密算法的研究. 物理学报, 2013, 62(8): 084202. doi: 10.7498/aps.62.084202
    [14] 汪先超, 闫镔, 刘宏奎, 李磊, 魏星, 胡国恩. 一种圆轨迹锥束CT中截断投影数据的高效重建算法. 物理学报, 2013, 62(9): 098702. doi: 10.7498/aps.62.098702
    [15] 王玉丹, 彭冠云, 佟亚军, 周光照, 任玉琦, 杨群, 肖体乔. 影响同步辐射X射线螺旋显微CT的若干因素研究. 物理学报, 2012, 61(5): 054205. doi: 10.7498/aps.61.054205
    [16] 刘慧强, 任玉琦, 周光照, 和友, 薛艳玲, 肖体乔. 相移吸收二元性算法用于X射线混合衬度定量显微CT的可行性研究. 物理学报, 2012, 61(7): 078701. doi: 10.7498/aps.61.078701
    [17] 罗召洋, 杨孝全, 孟远征, 邓勇. Micro CT中混叠伪影的消除. 物理学报, 2010, 59(11): 8237-8243. doi: 10.7498/aps.59.8237
    [18] 张 凯, 朱佩平, 黄万霞, 袁清习, 刘 力, 袁 斌, 王寯越, 舒 航, 陈 博, 刘宜晋, 李恩荣, 刘小松, 吴自玉. 代数迭代重建算法在折射衬度CT中的应用. 物理学报, 2008, 57(6): 3410-3418. doi: 10.7498/aps.57.3410
    [19] 戚霞枝, 郑少白. CT-6B托卡马克装置中软X射线辐射及扰动. 物理学报, 1984, 33(4): 465-471. doi: 10.7498/aps.33.465
    [20] 一○四组. CT-6托卡马克研究(Ⅱ)——物理实验结果. 物理学报, 1980, 29(6): 764-777. doi: 10.7498/aps.29.764
计量
  • 文章访问数:  3453
  • PDF下载量:  97
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-12-03
  • 修回日期:  2023-03-15
  • 上网日期:  2023-03-31
  • 刊出日期:  2023-06-05

/

返回文章
返回