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快速一阶方法的低剂量CT有序子集图像重建

毛宝林 陈晓朝 孝大宇 范晟昱 滕月阳 康雁

引用本文:
Citation:

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

毛宝林, 陈晓朝, 孝大宇, 范晟昱, 滕月阳, 康雁

Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy

Mao Bao-Lin, Chen Xiao-Zhao, Xiao Da-Yu, Fan Sheng-Yu, Teng Yue-Yang, Kang Yan
PDF
导出引用
  • 低剂量计算机断层成像(computed tomography,CT)具有减少X射线对患者的伤害的优势. 本文主要针对从不完备投影数据重建出高质量低剂量CT图像的问题. 通常,这个问题可以通过统计图像重建方法来实现,而统计重建算法需要非常多的迭代次数,导致了巨大的计算时间压力,以至于很难应用在实践中. 为解决此问题,本文提出一种有序子集重建算法,该算法结合了全变分最小化和快速一阶方法以减少重建的迭代次数,采用Split Bregman交替方向法求解上述优化问题,利用投影到凸集合的方法加快迭代的收敛速率. 实验结果表明,在同样的迭代次数下,本文提出的方法与基于有序子集的一阶方法相比较,相对重建误差的下降速度更快.
    Low-dose computed tomography(CT) has an advantage to reduce X-rays that are harmful to the body. This paper considers the issue of reconstructing high-quality low-dose CT images from incomplete projection data. Generally, this can be done by statistical image reconstruction methods. However, the huge number of iterations of the statistical reconstruction algorithms leads to long computing time, making them difficult to be of practical value. To solve this problem, we propose a method to alleviate the issue by using total variation minimization and fast first-order method for the ordered subsets. We use Split Bregman alternating direction method to solve the optimization problem. Then, the projection onto convex sets method is used to speed up the convergence rate of the iterative method. Numerical experiments show that the relative reconstruction error of the proposed method can decrease faster than the first-order method of ordered subsets with the same iterative number.
    • 基金项目: 国家自然科学基金(批准号:61372014,61201053,61302013)、高等学校博士学科点专项科研基金(批准号:20110042110036)和东北大学基础研究计划(批准号:N110619001)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61372014, 61201053, 61302013), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110042110036), and the Fundamental Research Project of Northeastern University, China (Grant No. 110619001).
    [1]

    Brenner D J, Hall E J 2007 New Engl. J. Med. 357 2277

    [2]

    Candès E J, Romberg J, Tao T 2006 IEEE Trans. Info. Theory 52 489

    [3]

    Candès E J, Tao T 2006 IEEE Trans. Info. Theory 52 5406

    [4]

    Donoho D 2006 IEEE Trans. Info. Theory 52 1289

    [5]

    Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2010 Chin. Phys.B 19 088106

    [6]

    Yang F Q, Zhang D H, Huang K D, Wang K, Xu Z 2014 Acta Phys. Sin. 63 058701 (in Chinese)[杨富强, 张定华, 黄魁东, 王鹍, 徐哲 2014 物理学报 63 058701]

    [7]

    Rudin L, Osher S, Fatemi E 1992 Physica D 60 259

    [8]

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

    [9]

    Gu Y F, Yan B, Li L, Wei F, Han Yu, Chen J 2014 Acta Phys. Sin. 63 018701 (in Chinese)[古宇飞, 闫镔, 李磊, 魏峰, 韩玉, 陈健 2014 物理学报 63 018701]

    [10]

    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J 2010 Foundations and Trends?in Machine Learning 3 1

    [11]

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

    [12]

    Wang L Y, Zhang H M, Cai A L, Yan B, Li L, Hu G E 2013 Acta Phys. Sin. 62 198701 (in Chinese)[王林元, 张瀚铭, 蔡爱龙, 闫镔, 李磊, 胡国恩 2013 物理学报 62 198701]

    [13]

    Ramani S, Fessler J A 2012 IEEE Trans. Med. Imag. 31 677

    [14]

    Matakos A, Ramani S, Fessler J A 2013 IEEE Trans. Image Process. 22 2019

    [15]

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

    [16]

    Sidky E Y, Jørgensen J S, Pan X 2013 Med. Phys. 40 031115

    [17]

    Nesterov Y E 1983 Dokl. Akad. Nauk SSSR 269 543 (in Russian)

    [18]

    Choi K, Wang J, Zhu L, Suh T S, Boyd S, Xing L 2010 Med. Phys. 37 5113

    [19]

    Jensen T L, Jørgensen J S, Hansen P C, Jensen S H 2012 BIT Numer. Math. 52 329

    [20]

    Beck A, Teboulle M 2009 SIAM J. Imaging Sci. 2 183

    [21]

    Daubechies I, Fornasier M, Loris I 2008 J. Fourier Anal. Appl. 14 764

    [22]

    Daubechies I, Defrise M, Mol C D 2004 Comm. Pure Appl. Math. 57 1413

    [23]

    Beck A, Teboulle M 2009 IEEE Trans. Image Process. 18 2419

    [24]

    Erdogan H, Fessler J A 1999 Phys. Med. Biol. 44 2835

    [25]

    Hudson H M, Larkin R S 1994 IEEE Trans. Med. Imag. 13 601

    [26]

    Kim D, Ramani S, Fessler J A 2013 The 12th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine California, USA, June 16-21, 2013 p22

  • [1]

    Brenner D J, Hall E J 2007 New Engl. J. Med. 357 2277

    [2]

    Candès E J, Romberg J, Tao T 2006 IEEE Trans. Info. Theory 52 489

    [3]

    Candès E J, Tao T 2006 IEEE Trans. Info. Theory 52 5406

    [4]

    Donoho D 2006 IEEE Trans. Info. Theory 52 1289

    [5]

    Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2010 Chin. Phys.B 19 088106

    [6]

    Yang F Q, Zhang D H, Huang K D, Wang K, Xu Z 2014 Acta Phys. Sin. 63 058701 (in Chinese)[杨富强, 张定华, 黄魁东, 王鹍, 徐哲 2014 物理学报 63 058701]

    [7]

    Rudin L, Osher S, Fatemi E 1992 Physica D 60 259

    [8]

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

    [9]

    Gu Y F, Yan B, Li L, Wei F, Han Yu, Chen J 2014 Acta Phys. Sin. 63 018701 (in Chinese)[古宇飞, 闫镔, 李磊, 魏峰, 韩玉, 陈健 2014 物理学报 63 018701]

    [10]

    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J 2010 Foundations and Trends?in Machine Learning 3 1

    [11]

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

    [12]

    Wang L Y, Zhang H M, Cai A L, Yan B, Li L, Hu G E 2013 Acta Phys. Sin. 62 198701 (in Chinese)[王林元, 张瀚铭, 蔡爱龙, 闫镔, 李磊, 胡国恩 2013 物理学报 62 198701]

    [13]

    Ramani S, Fessler J A 2012 IEEE Trans. Med. Imag. 31 677

    [14]

    Matakos A, Ramani S, Fessler J A 2013 IEEE Trans. Image Process. 22 2019

    [15]

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

    [16]

    Sidky E Y, Jørgensen J S, Pan X 2013 Med. Phys. 40 031115

    [17]

    Nesterov Y E 1983 Dokl. Akad. Nauk SSSR 269 543 (in Russian)

    [18]

    Choi K, Wang J, Zhu L, Suh T S, Boyd S, Xing L 2010 Med. Phys. 37 5113

    [19]

    Jensen T L, Jørgensen J S, Hansen P C, Jensen S H 2012 BIT Numer. Math. 52 329

    [20]

    Beck A, Teboulle M 2009 SIAM J. Imaging Sci. 2 183

    [21]

    Daubechies I, Fornasier M, Loris I 2008 J. Fourier Anal. Appl. 14 764

    [22]

    Daubechies I, Defrise M, Mol C D 2004 Comm. Pure Appl. Math. 57 1413

    [23]

    Beck A, Teboulle M 2009 IEEE Trans. Image Process. 18 2419

    [24]

    Erdogan H, Fessler J A 1999 Phys. Med. Biol. 44 2835

    [25]

    Hudson H M, Larkin R S 1994 IEEE Trans. Med. Imag. 13 601

    [26]

    Kim D, Ramani S, Fessler J A 2013 The 12th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine California, USA, June 16-21, 2013 p22

  • [1] 王磊, 李洪奇, 徐兴磊, 徐世民, 王继锁. 利用特殊函数和类比法有序化排列正负指数幂算符. 物理学报, 2021, 70(4): 040302. doi: 10.7498/aps.70.20201652
    [2] 齐伟华, 李壮志, 马丽, 唐贵德, 吴光恒, 胡凤霞. 磁性材料磁有序的分子场来源. 物理学报, 2017, 66(6): 067501. doi: 10.7498/aps.66.067501
    [3] 许永红, 石兰芳, 莫嘉琪. 强阻尼广义sine-Gordon方程特征问题的变分迭代法. 物理学报, 2015, 64(1): 010201. doi: 10.7498/aps.64.010201
    [4] 吴祝慧, 韩月琪, 钟中, 杜华栋, 王云峰. 基于区域逐步分析的集合变分资料同化方法. 物理学报, 2014, 63(7): 079201. doi: 10.7498/aps.63.079201
    [5] 古宇飞, 闫镔, 李磊, 魏峰, 韩玉, 陈健. 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. 物理学报, 2014, 63(1): 018701. doi: 10.7498/aps.63.018701
    [6] 韩月琪, 钟中, 王云峰, 杜华栋. 梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用. 物理学报, 2013, 62(4): 049201. doi: 10.7498/aps.62.049201
    [7] 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
    [8] 石明珠, 许廷发, 梁炯, 李相民. 单幅模糊图像点扩散函数估计的梯度倒谱分析方法研究. 物理学报, 2013, 62(17): 174204. doi: 10.7498/aps.62.174204
    [9] 方晟, 吴文川, 应葵, 郭华. 基于非均匀螺旋线数据和布雷格曼迭代的快速磁共振成像方法. 物理学报, 2013, 62(4): 048702. doi: 10.7498/aps.62.048702
    [10] 王广涛, 张敏平, 李珍, 郑立花. KCrF3中的轨道有序及其成因. 物理学报, 2012, 61(3): 037102. doi: 10.7498/aps.61.037102
    [11] 张荣, 徐振源, 杨永清. 通过同步实现"有序+有序=混沌"的例子. 物理学报, 2011, 60(1): 010515. doi: 10.7498/aps.60.010515
    [12] 刘忍肖, 陈胜利, 董鹏. 旋涂法快速制备双层二元胶体微球有序薄膜. 物理学报, 2009, 58(4): 2820-2828. doi: 10.7498/aps.58.2820
    [13] 王 凯, 杨 光, 龙 华, 李玉华, 戴能利, 陆培祥. 金纳米颗粒的有序制备及其光学特性. 物理学报, 2008, 57(6): 3862-3867. doi: 10.7498/aps.57.3862
    [14] 潘江陵, 倪 军. 面心立方(001)方向AB合金薄膜表面层的有序无序相变. 物理学报, 2006, 55(1): 413-418. doi: 10.7498/aps.55.413
    [15] 宋庆功, 丛选忠, 张庆军, 莫文玲, 戴占海. 六角蜂窝晶格的有序结构. 物理学报, 2000, 49(10): 2011-2016. doi: 10.7498/aps.49.2011
    [16] 曹万强, 成元发, 刘俊刁, 幸国坤. C60分子在有序-无序和玻璃态相变间的取向概率与弛豫行为. 物理学报, 2000, 49(10): 2001-2006. doi: 10.7498/aps.49.2001
    [17] 钟锡华, 朱亚芬. 无规排列功率谱的有序孔径角. 物理学报, 1992, 41(12): 1955-1960. doi: 10.7498/aps.41.1955
    [18] 王强, 顾秉林, 朱嘉麟, 张孝文. 用原子集团的有序-无序相变理论研究FexCu1-x系统的非晶相形成. 物理学报, 1989, 38(2): 273-279. doi: 10.7498/aps.38.273
    [19] 陆学善, 梁敬魁, 杨忠若. MnGa的晶体结构与有序度. 物理学报, 1979, 28(1): 54-54. doi: 10.7498/aps.28.54
    [20] 施士元, 张国焕. 无序到有序恒温转变的弛豫时间. 物理学报, 1956, 12(1): 80-82. doi: 10.7498/aps.12.80
计量
  • 文章访问数:  4345
  • PDF下载量:  463
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-03-31
  • 修回日期:  2014-05-05
  • 刊出日期:  2014-07-05

/

返回文章
返回