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抑制傅里叶变换法恢复的X射线相衬像中的伪影

杨君 吴浩 罗琨皓 郭金川 宗方轲

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抑制傅里叶变换法恢复的X射线相衬像中的伪影

杨君, 吴浩, 罗琨皓, 郭金川, 宗方轲

Suppression of artifacts in X-ray phase-contrast images retrieved by Fourier transform

Yang Jun, Wu Hao, Luo Kun-Hao, Guo Jin-Chuan, Zong Fang-Ke
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  • 在基于光栅的X射线相衬信号的恢复方法中, 主要有相移法和傅里叶变换法两种方法. 相移法具有精度高、噪声小的优点, 但由于至少需要三幅图像才能恢复出相衬信号, 样品所受的辐射剂量大. 而傅里叶变换法只需一幅图像即可恢复出物体的相衬信号, 具有快速、实时的优点, 但恢复出的信号精度低, 易受伪影影响. 因此, 本文利用两幅图像傅里叶变换法恢复X射线相衬信号, 该方法能够有效地抑制相衬信号中由于频谱混叠所产生的伪影. 另外, 通过增加载波条纹的频率, 能够拉大频域中的频谱间隔, 从而进一步抑制伪影的产生.
    Over the last two decades, the grating-based phase-contrast imaging has aroused the interest of a number of researchers. It could provide an access to three complementary signals simultaneously: the conventional absorption contrast, the differential phase contrast related to refraction of incident wave, and the dark-field contrast that relates to ultra small angle scattering in a sample. The grating-based phase-contrast signals have higher contrast sensitivity for some types of soft samples than the absorption signals. Dark-field signals have better diagnostic effects in the detection of lung tumors, pneumothorax and the identification of microcalcifications in breast. There are two main phase retrieval methods in grating-based X-ray phase-contrast imaging, i.e. phase stepping method and Fourier transform method. The phase signals retrieved by phase stepping is high precise and has low noise. But the sample suffers high dose due to at least three exposures. The phase signals retrieved by Fourier transform is low-dose due to the fact that only one image with sample is needed, but it is easily affected by artifacts when the size of the filtering window is too large. However, when the size of the filtering window is too small, the high-frequency information of the phase-contrast image will be lost, and the image will become blurred. A trade-off between definitions of the image and artifacts should be made. Since the phase-contrast signal and the dark-field signal of the sample are modulated by carrier fringes, the frequency spectrum of the detected image consists of many different harmonics. The artifacts in the retrieved signals originate from the spectrum aliasing between primary peak around zero spatial frequency and first-order harmonic peaks. Therefore, the subtraction between two images with phase difference can remove the primary peak, and the artifacts in the phase-contrast signals and dark-field signals will be suppressed. In order to further suppress the artifacts, we increase the frequency of carrier fringes, which results in a larger distance between first-order harmonic peaks in frequency domain. We finally attain artifact-free phase-contrast images and dark-field images while maintaining high definition of the images. The method proposed here is not only applicable to incoherent imaging system, but also to Talbot-Lau interferometer, and it would be useful in fast and low-dose X-ray phase-contrast and dark-field imaging.
      通信作者: 郭金川, jcguo@szu.edu.cn ; 宗方轲, zongfk168@163.com
    • 基金项目: 国家自然科学基金(批准号: 11674232)和广东省基础与应用基础研究基金(批准号: 2019A1515011785)资助的课题
      Corresponding author: Guo Jin-Chuan, jcguo@szu.edu.cn ; Zong Fang-Ke, zongfk168@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11674232) and Guangdong Provincial Basic and Applied Basic Research Foundation, China (Grant No. 2019A1515011785)
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    Momose A, Kawamoto S, Koyama I, Hamaishi Y, Takai K, Suzuki Y 2003 Jpn. J. Appl. Phys. 42 L866Google Scholar

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    Pfeiffer F, Weitkamp T, Bunk O, David C 2006 Nat. Phys. 2 258Google Scholar

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    Pfeiffer F, Bech M, Bunk O, Kraft P, Eikenberry E F, Bronnimann C, Grunzweig C, David C 2008 Nat. Mater. 7 134Google Scholar

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    Bech M, Tapfer A, Pauwels B, Bruyndonckx P, Sasov A, Pfeiffer F 2013 Sci. Rep. 3 3209Google Scholar

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    Anton G, Michel T, Pelzer G, Radicke M, Rieger J, Weber T 2013 Z. Med. Phys. 23 228Google Scholar

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    Weitkamp T, Diaz A, David C, Pfeiffer F, Stampanoni M, Cloetens P, Ziegler E 2005 Opt. Express 13 6296Google Scholar

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    Takeda M, Ina H, Kobayashi S 1982 J. Opt. Soc. Am. 72 156Google Scholar

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    Wen H, Bennett E E, Hegedus M M, Rapacchi S 2009 Radiology 251 910Google Scholar

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    Lim H, Park Y, Cho H, Je U, Hong D, Park C, Woo T, Lee M, Kim J, Chung N, Kim J, Kim J 2015 Opt. Commun. 348 85Google Scholar

    [13]

    Lim H W, Lee H W, Cho H S, Je U K, Park C K, Kim K S, Kim G A, Park S Y, Lee D Y, Park Y O, Woo T H, Lee S H, Chung W H, Kim J W, Kim J G 2017 Nucl. Instrum. Methods Phys. Res., Sect. A 850 89Google Scholar

    [14]

    Lim H, Lee H, Cho H, Seo C, Je U, Park C, Kim K, Kim G, Park S, Lee D, Kang S, Lee M 2017 J. Korean Phys. Soc. 71 722Google Scholar

    [15]

    Seifert M, Gallersdörfer M, Ludwig V, Schuster M, Horn F, Pelzer G, Rieger J, Michel T, Anton G 2018 J. Imaging 4 62Google Scholar

    [16]

    Seifert M, Ludwig V, Gallersdorfer M, Hauke C, Hellbach K, Horn F, Pelzer G, Radicke M, Rieger J, Sutter S M, Michel T, Anton G 2018 Phys. Med. Biol. 63 185010Google Scholar

    [17]

    Li J, Su X Y, Guo L R 1990 Opt. Eng. 29 1439Google Scholar

    [18]

    陈文静, 苏显渝, 曹益平, 向立群 2004 中国激光 31 740Google Scholar

    Chen W J, Su X Y, Cao Y P, Xiang L Q 2004 Chin. J. Las. 31 740Google Scholar

    [19]

    Zhu P, Zhang K, Wang Z, Liu Y, Liu X, Wu Z, McDonald S A, Marone F, Stampanoni M 2010 Proc. Natl. Acad. Sci. U. S. A. 107 13576Google Scholar

    [20]

    Wang Z, Gao K, Ge X, Wu Z, Chen H, Wang S, Zhu P, Yuan Q, Huang W, Zhang K, Wu Z 2013 J. Phys. D: Appl. Phys. 46 494003Google Scholar

    [21]

    杜杨, 雷耀虎, 刘鑫, 郭金川, 牛憨笨 2013 物理学报 62 06872Google Scholar

    Yang D, Lei Y H, Liu X, Guo J C, Niu H B 2013 Acta Phys. Sin. 62 06872Google Scholar

    [22]

    Momose A, Yashiro W, Takeda Y, Suzuki Y, Hattori T 2006 Jpn. J. Appl. Phys. 45 5254Google Scholar

  • 图 1  非相干X射线成像系统示意图

    Fig. 1.  Schematic diagram of incoherent X-ray imaging.

    图 2  一般情形下载波条纹的频谱图

    Fig. 2.  The Fourier spectrum of carrier fringe patterns in general case.

    图 3  实际情况下发生的频谱混叠

    Fig. 3.  Spectrum aliasing between different harmonic peaks in practice.

    图 4  频谱混叠对恢复出相位的影响 (a), (b)和(c)分别代表载波条纹周期与探测器像素尺寸比值r为3, 4和5时的情形

    Fig. 4.  The impact of spectrum aliasing on phase retrieval. (a), (b) and (c) denote the cases, in which the ratios of the carrier fringe period to size of detector pixel are 3, 4 and 5, respectively.

    图 5  无频谱混叠时恢复出来的相位分布

    Fig. 5.  The phase retrieval when no spectrum aliasing.

    图 6  (a) 两幅图像傅里叶变换法所恢复出的PMMA相衬像; (b)单幅图像傅里叶变换法所恢复出的PMMA相衬像

    Fig. 6.  (a) The phase-contrast image of PMMA retrieved by Fourier transform with two images; (b) the phase-contrast image of PMMA retrieved by Fourier transform with one image.

    图 7  (a) 图6中白色方框区域按行取平均后绘制的曲线; (b) 图6中黑色方框区域按行取平均后绘制的曲线

    Fig. 7.  (a) Curves from averaging the area of white rectangle in figure 6 by row; (b) curves from averaging the area of black rectangle in Figure 6 by row.

    图 8  载波条纹周期与探测器像素尺寸比值r = 3时, 鸡翅的频谱 (a)、相衬像(c)和暗场像(e). r = 5时, 鸡翅的频谱(b)、相衬像(d)和暗场像(f)

    Fig. 8.  Fourier spectrum (a), phase-contrast image (c) and dark-field image (e) of a chicken wing when r = 3. Fourier spectrum (b), phase-contrast image (d) and dark-field image (f) of a chicken wing when r = 5.

    表 1  两种不同傅里叶变换方法的定量比较

    Table 1.  Quantitative comparison between two kinds of Fourier transform algorithms.

    背景相位
    均值/rad
    背景相位标
    准差/rad
    横截面峰
    峰值/rad
    单幅图像
    傅里叶变换
    0.35020.00590.2412
    两幅图像
    傅里叶变换
    0.25260.00170.1112
    下载: 导出CSV
  • [1]

    David C, Nohammer E, Solak H H, Ziegler E 2002 Appl. Phys. Lett. 81 3287Google Scholar

    [2]

    Momose A, Kawamoto S, Koyama I, Hamaishi Y, Takai K, Suzuki Y 2003 Jpn. J. Appl. Phys. 42 L866Google Scholar

    [3]

    Pfeiffer F, Weitkamp T, Bunk O, David C 2006 Nat. Phys. 2 258Google Scholar

    [4]

    Pfeiffer F, Bech M, Bunk O, Kraft P, Eikenberry E F, Bronnimann C, Grunzweig C, David C 2008 Nat. Mater. 7 134Google Scholar

    [5]

    Bech M, Tapfer A, Pauwels B, Bruyndonckx P, Sasov A, Pfeiffer F 2013 Sci. Rep. 3 3209Google Scholar

    [6]

    Anton G, Michel T, Pelzer G, Radicke M, Rieger J, Weber T 2013 Z. Med. Phys. 23 228Google Scholar

    [7]

    Yang J, Guo J C, Lei Y H, Yi M H, Chen L 2017 Chin. Phys. B 26 028701Google Scholar

    [8]

    Weitkamp T, Diaz A, David C, Pfeiffer F, Stampanoni M, Cloetens P, Ziegler E 2005 Opt. Express 13 6296Google Scholar

    [9]

    Takeda M, Ina H, Kobayashi S 1982 J. Opt. Soc. Am. 72 156Google Scholar

    [10]

    Wen H, Bennett E E, Hegedus M M, Carroll S C 2008 IEEE Trans. Med. Imaging 27 997Google Scholar

    [11]

    Wen H, Bennett E E, Hegedus M M, Rapacchi S 2009 Radiology 251 910Google Scholar

    [12]

    Lim H, Park Y, Cho H, Je U, Hong D, Park C, Woo T, Lee M, Kim J, Chung N, Kim J, Kim J 2015 Opt. Commun. 348 85Google Scholar

    [13]

    Lim H W, Lee H W, Cho H S, Je U K, Park C K, Kim K S, Kim G A, Park S Y, Lee D Y, Park Y O, Woo T H, Lee S H, Chung W H, Kim J W, Kim J G 2017 Nucl. Instrum. Methods Phys. Res., Sect. A 850 89Google Scholar

    [14]

    Lim H, Lee H, Cho H, Seo C, Je U, Park C, Kim K, Kim G, Park S, Lee D, Kang S, Lee M 2017 J. Korean Phys. Soc. 71 722Google Scholar

    [15]

    Seifert M, Gallersdörfer M, Ludwig V, Schuster M, Horn F, Pelzer G, Rieger J, Michel T, Anton G 2018 J. Imaging 4 62Google Scholar

    [16]

    Seifert M, Ludwig V, Gallersdorfer M, Hauke C, Hellbach K, Horn F, Pelzer G, Radicke M, Rieger J, Sutter S M, Michel T, Anton G 2018 Phys. Med. Biol. 63 185010Google Scholar

    [17]

    Li J, Su X Y, Guo L R 1990 Opt. Eng. 29 1439Google Scholar

    [18]

    陈文静, 苏显渝, 曹益平, 向立群 2004 中国激光 31 740Google Scholar

    Chen W J, Su X Y, Cao Y P, Xiang L Q 2004 Chin. J. Las. 31 740Google Scholar

    [19]

    Zhu P, Zhang K, Wang Z, Liu Y, Liu X, Wu Z, McDonald S A, Marone F, Stampanoni M 2010 Proc. Natl. Acad. Sci. U. S. A. 107 13576Google Scholar

    [20]

    Wang Z, Gao K, Ge X, Wu Z, Chen H, Wang S, Zhu P, Yuan Q, Huang W, Zhang K, Wu Z 2013 J. Phys. D: Appl. Phys. 46 494003Google Scholar

    [21]

    杜杨, 雷耀虎, 刘鑫, 郭金川, 牛憨笨 2013 物理学报 62 06872Google Scholar

    Yang D, Lei Y H, Liu X, Guo J C, Niu H B 2013 Acta Phys. Sin. 62 06872Google Scholar

    [22]

    Momose A, Yashiro W, Takeda Y, Suzuki Y, Hattori T 2006 Jpn. J. Appl. Phys. 45 5254Google Scholar

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出版历程
  • 收稿日期:  2020-10-27
  • 修回日期:  2020-12-11
  • 上网日期:  2021-05-09
  • 刊出日期:  2021-05-20

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