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

基于全变分最小化和交替方向法的康普顿散射成像重建算法

古宇飞 闫镔 李磊 魏峰 韩玉 陈健

引用本文:
Citation:

基于全变分最小化和交替方向法的康普顿散射成像重建算法

古宇飞, 闫镔, 李磊, 魏峰, 韩玉, 陈健

Image reconstruction based on total variation minimization and alternating direction method for Compton scatter tomography

Gu Yu-Fei, Yan Bin, Li Lei, Wei Feng, Han Yu, Chen Jian
PDF
导出引用
  • 康普顿散射成像技术利用射线与物质作用后的散射光子信息对物质的电子密度进行成像. 与传统的透射成像方式相比,康普顿散射成像具有系统结构灵活、成像对比度高、辐射剂量低等优势,在无损检测、医疗诊断、安全检查等领域有着广阔的应用前景. 但其重建问题是一个非线性的逆问题,通常是不适定的,其解对噪声和测量误差非常敏感. 为解决此问题,本文结合全变分最小化正则化方法和交替方向法提出了一种新的康普顿散射成像重建算法. 该算法首先将问题对应的TV模型转化为与之等价的带约束的优化问题,然后利用增广拉格朗日乘子法将优化问题分解为两个具有解析解的子问题,并通过交替求解子问题使增广拉格朗日函数达到最小,进而得到重建的图像. 在仿真实验中,通过与主流的ASD-POCS方法进行对比,证明了该算法在重建精度和重建效率方面的优势.
    Compton scatter tomography measures samples electron densities utilizing the scattered photons. Compared to traditional transmission imaging models, Compton scatter tomography has the following characteristics, i.e. freedom in construction systems, greater sensitivity for low-density materials, and lower radiation dose. It has been applied in non-destructive testing, medical, and security inspections, and other fields. However, Compton scatter tomography reconstruction is a nonlinear inverse problem, common is ill-posed, and its solutions are very sensitive to noise and erroneous measurements. To tackle the problem, in this paper we propose a novel Compton scatter tomography reconstruction algorithm based on the total variation minimization and alternating direction method. The main idea of our method is to reformulate the reconstruction problems TV function as an optimization with constrains where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method to solve the sub-problems. Numerical experiments shows that the reconstruction quality and efficiency of the proposed method are improved compared to the adaptive-steepest-descent-projection onto convex sets method.
    • 基金项目: 国家高技术研究发展计划(批准号:2012AA011603)和国家自然科学基金(批准号:61372172)资助的课题.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603), and the National Natural Science Foundation of China (Grant No. 61372172).
    [1]

    Tang S S, Hussein E M A 2004 Appl. Radiat.Isot. 61 3

    [2]

    Hussein E M A, Desrosiers M, Waller E J 2005 Radiat. Phys. Chem. 73 7

    [3]

    Evans B L, Martin J B, Burggraf L W, Roggemann M C, Hangartner T N 2002 Nuclear Instruments and Methods in Physics Research A 480 797

    [4]

    Harding G, Harding E 2010 Appl. Radiat. Isot. 68 993

    [5]

    Harding G 2004 Radiat. Phys. Chem. 71 869

    [6]

    Faysal E K, Ilan Y, Hussein E M A 2003 Phys. Med. Biol. 48 3445

    [7]

    Pistolesi M, Miniati M 1981 Nucl. Med. All. Sci. 25 182

    [8]

    Shin W P, Sunwoo Y, Jun S R 2006 Nuclear Instruments and Methods 568 369

    [9]

    Michael D H, Joseph J M, Dennis G L, Gary L C 1994 IEEE T. Med. Imaging 13 461

    [10]

    Lale P G 1959 Phys. Med. Biol. 18 532

    [11]

    Wang J J, Huang X W, Zhong X R 2004 Chinese Journal of Scientific Instrument 25 164 (in Chinese) [王加俊, 黄贤武, 仲兴荣 2004 仪器仪表学 25 164]

    [12]

    Truong T T, Nguyen M K 2011 Inverse Problems 27 1

    [13]

    Farmer F T, Collins M P 1971 Phys. Med. Bio. 16 577

    [14]

    Kondic N N, Jacobs A M, Ebert D 1983 American Nuclear Society 2 1443

    [15]

    Hussein E M, AMeneley D A, Banerjee S 1986 Nucl. Sci. Eng. 92 341

    [16]

    Arendtsz N V, Hussein E M A 1995 IEEE Trans. Nucl. Sci. 42 2155

    [17]

    Wang J J, Huang X W, Zhao R 2004 Microelectronics & Computer 21 95 (in Chinese) [王加俊, 黄贤武, 赵然 2004 微电子学与计算机 21 95]

    [18]

    ArendtszN V, HusseinE M A 1993 SPIE Vol. 2035 Mathematical Methods in Medical Imaging Ⅱ San Diego, CA, July, 1993 p230

    [19]

    Li S P, Wang L Y, Yan B, Li L, Liu Y J 2012 Chin. Phys. B 21 108703

    [20]

    Candes E, Tao T 2006 IEEE Trans. Inf. Theory 52 5406

    [21]

    Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489

    [22]

    Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777

    [23]

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

    [24]

    Li C B 2009 MS Dissertation (Houston: Rice University)

    [25]

    Wang Y L, Yang J F, Yin W T, Zhang Y 2008 SIAM J. Imag. Sci. 1 248

  • [1]

    Tang S S, Hussein E M A 2004 Appl. Radiat.Isot. 61 3

    [2]

    Hussein E M A, Desrosiers M, Waller E J 2005 Radiat. Phys. Chem. 73 7

    [3]

    Evans B L, Martin J B, Burggraf L W, Roggemann M C, Hangartner T N 2002 Nuclear Instruments and Methods in Physics Research A 480 797

    [4]

    Harding G, Harding E 2010 Appl. Radiat. Isot. 68 993

    [5]

    Harding G 2004 Radiat. Phys. Chem. 71 869

    [6]

    Faysal E K, Ilan Y, Hussein E M A 2003 Phys. Med. Biol. 48 3445

    [7]

    Pistolesi M, Miniati M 1981 Nucl. Med. All. Sci. 25 182

    [8]

    Shin W P, Sunwoo Y, Jun S R 2006 Nuclear Instruments and Methods 568 369

    [9]

    Michael D H, Joseph J M, Dennis G L, Gary L C 1994 IEEE T. Med. Imaging 13 461

    [10]

    Lale P G 1959 Phys. Med. Biol. 18 532

    [11]

    Wang J J, Huang X W, Zhong X R 2004 Chinese Journal of Scientific Instrument 25 164 (in Chinese) [王加俊, 黄贤武, 仲兴荣 2004 仪器仪表学 25 164]

    [12]

    Truong T T, Nguyen M K 2011 Inverse Problems 27 1

    [13]

    Farmer F T, Collins M P 1971 Phys. Med. Bio. 16 577

    [14]

    Kondic N N, Jacobs A M, Ebert D 1983 American Nuclear Society 2 1443

    [15]

    Hussein E M, AMeneley D A, Banerjee S 1986 Nucl. Sci. Eng. 92 341

    [16]

    Arendtsz N V, Hussein E M A 1995 IEEE Trans. Nucl. Sci. 42 2155

    [17]

    Wang J J, Huang X W, Zhao R 2004 Microelectronics & Computer 21 95 (in Chinese) [王加俊, 黄贤武, 赵然 2004 微电子学与计算机 21 95]

    [18]

    ArendtszN V, HusseinE M A 1993 SPIE Vol. 2035 Mathematical Methods in Medical Imaging Ⅱ San Diego, CA, July, 1993 p230

    [19]

    Li S P, Wang L Y, Yan B, Li L, Liu Y J 2012 Chin. Phys. B 21 108703

    [20]

    Candes E, Tao T 2006 IEEE Trans. Inf. Theory 52 5406

    [21]

    Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489

    [22]

    Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777

    [23]

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

    [24]

    Li C B 2009 MS Dissertation (Houston: Rice University)

    [25]

    Wang Y L, Yang J F, Yin W T, Zhang Y 2008 SIAM J. Imag. Sci. 1 248

  • [1] 潘新宇, 毕筱雪, 董政, 耿直, 徐晗, 张一, 董宇辉, 张承龙. 叠层相干衍射成像算法发展综述. 物理学报, 2023, 72(5): 054202. doi: 10.7498/aps.72.20221889
    [2] 董旭, 黄永盛, 唐光毅, 陈姗红, 司梅雨, 张建勇. 基于微波-电子康普顿背散射的环形正负电子对撞机束流能量测量方案. 物理学报, 2021, 70(13): 131301. doi: 10.7498/aps.70.20202081
    [3] 席晓琦, 韩玉, 李磊, 闫镔. 螺旋锥束计算机断层成像倾斜扇束反投影滤波局部重建算法. 物理学报, 2019, 68(8): 088701. doi: 10.7498/aps.68.20190055
    [4] 宋张勇, 于得洋, 蔡晓红. 康普顿相机的成像分辨分析与模拟. 物理学报, 2019, 68(11): 118701. doi: 10.7498/aps.68.20182245
    [5] 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
    [6] 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
    [7] 马永朋, 赵小利, 刘亚伟, 徐龙泉, 康旭, 倪冬冬, 闫帅, 朱林繁, 杨科. NO与C2H2的康普顿轮廓研究. 物理学报, 2015, 64(15): 153302. doi: 10.7498/aps.64.153302
    [8] 谢正超, 王飞, 严建华, 岑可法. 炉膛三维温度场重建中Tikhonov正则化和截断奇异值分解算法比较. 物理学报, 2015, 64(24): 240201. doi: 10.7498/aps.64.240201
    [9] 王飞, 魏兵, 杨谦, 李林茜. 基于Newmark算法的任意磁化方向铁氧体电磁散射时域有限差分分析. 物理学报, 2014, 63(16): 164101. doi: 10.7498/aps.63.164101
    [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] 夏少军, 陈林根, 戈延林, 孙丰瑞. 等温节流过程积耗散最小化. 物理学报, 2013, 62(18): 180202. doi: 10.7498/aps.62.180202
    [12] 邓勇, 张喧轩, 罗召洋, 许军, 杨孝全, 孟远征, 龚辉, 骆清铭. 融合结构先验信息的稳态扩散光学断层成像重建算法研究. 物理学报, 2013, 62(1): 014202. doi: 10.7498/aps.62.014202
    [13] 王林元, 张瀚铭, 蔡爱龙, 闫镔, 李磊, 胡国恩. 非精确交替方向总变分最小化重建算法. 物理学报, 2013, 62(19): 198701. doi: 10.7498/aps.62.198701
    [14] 周光照, 王玉丹, 任玉琦, 陈灿, 叶琳琳, 肖体乔. 相干X射线衍射成像三维重建的数字模拟研究. 物理学报, 2012, 61(1): 018701. doi: 10.7498/aps.61.018701
    [15] 李俊昌, 彭祖杰, Tankam Patrice, Picart Pascal. 散射光彩色数字全息光学系统及波面重建算法研究. 物理学报, 2010, 59(7): 4646-4655. doi: 10.7498/aps.59.4646
    [16] 葛愉成. 激光-电子康普顿散射物理特性研究. 物理学报, 2009, 58(5): 3094-3103. doi: 10.7498/aps.58.3094
    [17] 鄢 舒, 王 殊. 多原子分子气体中声波弛豫衰减谱的重建算法. 物理学报, 2008, 57(7): 4282-4291. doi: 10.7498/aps.57.4282
    [18] 闫玉波, 李清亮, 吴振森. 一种新时域交替隐式差分算法在散射问题中的应用. 物理学报, 2004, 53(12): 4173-4180. doi: 10.7498/aps.53.4173
    [19] 吕景发. 在相对论性电子上康普顿散射的极化自旋关联现象. 物理学报, 1965, 21(11): 1927-1932. doi: 10.7498/aps.21.1927
    [20] 徐永昌, 郑林生. 在γ-γ符合测量中康普顿散射所引起的符合. 物理学报, 1958, 14(2): 114-120. doi: 10.7498/aps.14.114
计量
  • 文章访问数:  4765
  • PDF下载量:  773
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-05-20
  • 修回日期:  2013-09-17
  • 刊出日期:  2014-01-05

/

返回文章
返回