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

基于稀疏优化的计算机断层成像图像不完全角度重建综述

王林元 刘宏奎 李磊 闫镔 张瀚铭 蔡爱龙 陈建林 胡国恩

引用本文:
Citation:

基于稀疏优化的计算机断层成像图像不完全角度重建综述

王林元, 刘宏奎, 李磊, 闫镔, 张瀚铭, 蔡爱龙, 陈建林, 胡国恩

Review of sparse optimization-based computed tomography image reconstruction from few-view projections

Wang Lin-Yuan, Liu Hong-Kui, Li Lei, Yan Bin, Zhang Han-Ming, Cai Ai-Long, Chen Jian-Lin, Hu Guo-En
PDF
导出引用
  • 计算机断层成像(computed tomography,CT)技术在医学和工业无损检测中都具有非常广泛的应用,CT重建算法是其中的核心,而不完全角度重建问题则是实际应用中重建算法研究领域的一个热点和难点问题. 近年来,随着稀疏优化理论与算法的飞速发展,基于稀疏优化的重建算法已经在不完全角度重建问题中得到了较广泛的应用,且表现出了良好的精度与速度性能. 本文首先对稀疏优化的基本理论结论与常用算法进行了介绍;而后对稀疏优化理论在CT图像不完全角度重建中的应用进行归纳,分类介绍了其主要研究成果及稀疏优化所发挥的作用;最后对基于稀疏优化的不完全角度重建研究进行了展望.
    Computed tomography (CT) is a technology widely used in medicine and industrial non-destructive testing, and the image reconstruction algorithm is a core technology of CT. Now, the image reconstruction from few-view projections is a hot point in the study of reconstruction algorithm. With the advancements in theories and algorithms, the sparse optimization has recently been applied to few-view reconstruction for CT image, and shown to have a good performance in both accuracy and speed. In this paper, basic conclusions and classical algorithms in sparse optimization are introduced. Furthermore, the spare optimization based few-view reconstruction algorithms for CT image, in particular the main results and the values of spare optimization, are summarized. Finally, the future research direction of sparse optimization based few-view reconstruction for CT image is discussed.
    • 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]

    Pan X, Sidky E Y, Vannier M 2009 Inverse Prob. 25 123009

    [2]

    Xu Q 2012 Ph. D. Dissertation (Xi'an: Xi'an Jiaotong University) (in Chinese) [许琼 2012 博士学位论文 (西安: 西安交通大学)]

    [3]
    [4]
    [5]

    Tuy H 1983 SIAM J. Appl. Math. 43 546

    [6]

    Smith B D 1985 IEEE Trans. Med. Imag. 4 14

    [7]
    [8]

    Heffernan P B, Robb R A 1983 IEEE Trans. Biomed. Eng. 30 838

    [9]
    [10]
    [11]

    Sezan M I, Stark H 1984 IEEE Trans. Med. Imag. 3 91

    [12]
    [13]

    Reis M L, Roberty N C 1992 Inverse Prob. 8 623

    [14]

    La Riviere P J, Pan X 1999 SPIE Proceeding Medical Imaging 1999: Physics of Medical Imaging San Diego, USA, February 20-26, 1999 p398

    [15]
    [16]

    Zhong Z G, Mei Y C, Wang Y P 1992 J. Wuhan Univ. (Nat. Sci. Ed.) 38 48 (in Chinese) [钟志刚, 梅雁诚, 王延平 1992 武汉大学学报(自然科学版) 38 48]

    [17]
    [18]

    L H, Li S G, Xu W Z, Yan X, L Y 1997 J. Chongqing Univ. 20 41 (in Chinese) [吕红, 李时光, 徐问之, 闫旭, 吕怡 1997 重庆大学学报 20 41]

    [19]
    [20]
    [21]

    Duan X H, Zhang L, Chen Z Q, Cheng J P 2007 Computerized Tomography Theory and Applications 16 1 (in Chinese) [段新辉, 张丽, 陈志强, 程建平 2007 CT理论与应用研究 16 1]

    [22]
    [23]

    Que J M, Wang Y F, Sun C L, Wei C F, Shi R J, Wei L 2012 Computerized Tomography Theory and Applications 21 169 (in Chinese) [阙介民, 王燕芳, 孙翠丽, 魏存峰, 史戎坚, 魏龙 2012 CT理论与应用研究 21 169]

    [24]

    Hunink M G M, Gazelle G S 2003 J. Clin. Invest. 111 1612

    [25]
    [26]
    [27]

    Imhof H, Schibany N, Ba-Ssalamah A, Czerny C, Hojreh A, Kainberger F, Krestan C, Kudler H, Nbauer I, Nowotny R 2003 Eur. J. Radiol. 47 29

    [28]

    Liu Y, Zhang H 2008 Chin. J. Med. Imaging Technol. 24 17 (in Chinese) [刘勇, 张华 2008 中国医学影像技术 24 17]

    [29]
    [30]

    Wang L Y 2010 M. S. Dissertation (Zhengzhou: PLA Information Engineering University) (in Chinese) [王林元 2010 硕士学位论文 (郑州: 解放军信息工程大学)]

    [31]
    [32]
    [33]

    Guo W 2011 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [郭威 2011 博士学位论文 (长春: 吉林大学)]

    [34]
    [35]

    Guo Q 2008 M. S. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [郭琦 2008 硕士学位论文 (合肥: 中国科学技术大学)]

    [36]

    Hu X Z 2008 M. S. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [胡小舟 2008 硕士学位论文 (合肥: 中国科学技术大学)]

    [37]
    [38]

    Kouris K, Tuy H, Lent A, Herman G T, Lewitt R M 1982 IEEE Trans. Med. Imag. 1 161

    [39]
    [40]

    Sidky E Y, Kao C M, Pan X 2006 J. X-ray Sci. Technol. 14 119

    [41]
    [42]
    [43]

    Liu N 2011 M. S. Dissertation (Guangzhou: Southern Medical University) (in Chinese) [刘楠 2011 硕士学位论文 (广州: 南方医科大学)]

    [44]
    [45]

    Liu W L 2013 M. S. Dissertation (Xi'an: Fourth Military Medical University) (in Chinese) [刘文磊 2013 硕士学位论文 (西安: 第四军医大学)]

    [46]
    [47]

    Inouye T 1979 IEEE Trans. Nucl. Sci. 26 2666

    [48]
    [49]

    Tam K C, Perez-Mendes V 1981 J. Opt. Soc. Am. 71 582

    [50]
    [51]

    Andersen A H 1989 IEEE Trans. Med. Imag. 8 50

    [52]
    [53]

    Gao H W, Zhang L, Chen Z Q, Cheng J P 2006 Computerized Tomography Theory and Applications 15 46 (in Chinese) [高河伟, 张丽, 陈志强, 程建平 2006 CT理论与应用研究15 46]

    [54]

    Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2009 Computerized Tomography Theory and Applications 18 22 (in Chinese) [王林元, 李磊, 闫镔, 江成顺, 王浩宇, 包尚联 2009 CT理论与应用研究 18 22]

    [55]
    [56]

    Jiao L C, Yang S Y, Liu F, Hou B 2011 Acta Electron. Sin. 39 1651 (in Chinese) [焦李成, 杨淑媛, 刘芳, 侯彪 2011 电子学报 39 1651]

    [57]
    [58]

    Wen Z W, Yin W T, Liu X, Zhang Y 2012 Oper. Res. Trans. 16 49 (in Chinese) [文再文, 印卧涛, 刘歆, 张寅 2012 运筹学学报 16 49]

    [59]
    [60]
    [61]

    Donoho D L 2006 Commun. Pure Appl. Math. 59 797

    [62]
    [63]

    Natarajin B K 1995 SIAM J. Comput. 24 227

    [64]

    Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289

    [65]
    [66]
    [67]

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

    [68]

    Candes E J, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [69]
    [70]
    [71]

    Donoho D L, Elad M 2003 Proc. Nat. Acad. Sci. USA 100 2197

    [72]
    [73]

    Gribonval R, Nielsen M 2003 IEEE Trans. Inf. Theory 49 3320

    [74]

    Zhang Y 2008 Rice University CAAM Tech. Rep. 2008-11

    [75]
    [76]

    Candes E J, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [77]
    [78]

    Candes E J 2008 CR Math. 346 589

    [79]
    [80]
    [81]

    Blanchard J, Cartis C, Tanner J 2009 IEEE Sig. Proc. Lett. 16 572

    [82]

    Candes E J 2007 IEEE Signal Proc. Mag. 24 21

    [83]
    [84]
    [85]
    [86]

    Figueiredo M, Nowak R, Wright S 2007 IEEE J. Sel. Top. Signal Process. 1 586

    [87]
    [88]

    Hale E, Yin W, Zhang Y 2008 SIAM J. Optimiz. 19 1107

    [89]
    [90]

    Hale E, Yin W, Zhang Y 2010 J. Comput. Math. 28 170

    [91]

    Wright S J, Nowak R D, Figueiredo M A T 2009 IEEE Trans. Sig. Proc. 57 2479

    [92]
    [93]
    [94]

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

    [95]

    Yun S, Toh K 2011 Comput. Optim. Appl. 48 273

    [96]
    [97]
    [98]

    Friedlander M, Vandenberg E 2008 SIAM J. Sci. Comput. 31 890

    [99]
    [100]

    Becker S, Bobin J, Candes E J 2011 SIAM J. Imag. Sci. 4 1

    [101]

    Yang J, Zhang Y 2011 SIAM J. Sci. Comput. 33 250

    [102]
    [103]
    [104]

    Deng W, Yin W, Zhang Y 2011 Rice University CAAM Tech. Rep. 2011-06

    [105]

    Gabay D, Mercier B 1976 Comput. Math. Appl. 2 17

    [106]
    [107]

    Hager W W, Hearn D W, Pardalos P M 1993 Large Scale Optimization: State of the Art (California: Springer US Press) p119

    [108]
    [109]
    [110]

    Chen G, Teboulle M 1994 Math. Program. 64 81

    [111]

    Wang Y, Yin W 2010 SIAM J. Imag. Sci. 3 856

    [112]
    [113]

    Li C, Yin W, Jiang H, Zhang Y 2012 Rice University CAAM Tech. Rep. 2012-13

    [114]
    [115]
    [116]

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

    [117]
    [118]
    [119]

    Parikh N, Boyd S 2014 Math. Prog. Comp. 6 77

    [120]
    [121]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 IEEE Trans. Sig. Proc. 60 1942

    [122]
    [123]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, March 25-30, 2012 p2869

    [124]
    [125]
    [126]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2013 IEEE Trans. Sig. Proc. 61 2718

    [127]
    [128]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of 51st IEEE Conference on Decision and Control (CDC) Hawaiian Islands, USA, December 10-13, 2012 p5116

    [129]
    [130]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of 51st IEEE Conference on Decision and Control (CDC) Hawaiian Islands, USA, December 10-13, 2012 p5110

    [131]
    [132]
    [133]

    Deng W, Yin W 2012 Rice University CAAM Tech. Rep. 2012-14

    [134]
    [135]
    [136]

    Shi W, Ling Q, Yuan K, Wu G, Yin W 2013 Proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP) Vancouver, Canada, May 26-31, 2013 p4613

    [137]
    [138]
    [139]

    Deng W, Lai M, Yin W 2013 UCLA CAM Tech. Rep. 2013-64

    [140]
    [141]

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

    [142]
    [143]

    Jin X, Li L, Chen Z, Zhang L, Xing Y 2010 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, Knoxville, USA, October 30- November 6, 2010 p2232

    [144]
    [145]

    Xu Q, Mou X, Tang S, Zhang Y 2010 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference Knoxville, USA, October 30-November 6, 2010 p3241

    [146]
    [147]

    Debatin M, Zygmanski P, Stsepankou D, Hesser J 2012 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference Anaheim, USA, October 27-November 3, 2012 p2295

    [148]

    Chen Z, Jin X, Li L, Wang G 2013 Phys. Med. Biol. 58 2119

    [149]
    [150]
    [151]

    Lian Q S, Hao P P 2009 Opt. Tech. 35 422 (in Chinese) [练秋生, 郝鹏鹏 2009 光学技术 35 422]

    [152]
    [153]

    Zou J, Sun Y Q, Zhang P 2009 Acta Opt. Sin. 29 1198 (in Chinese) [邹晶, 孙艳勤, 张朋 2009 光学学报 29 1198]

    [154]

    Yu H, Wang G 2010 Phys. Med. Biol. 55 3905

    [155]
    [156]

    Bian J, Siewerdsen J H, Han X, Sidky E Y, Prince J L, Pelizzari C A, Pan X 2010 Phys. Med. Biol. 55 6575

    [157]
    [158]
    [159]

    Han X, Bian J, Eaker D R, Kline T L, Sidky E Y, Ritman E L, Pan X 2011 IEEE Trans. Med. Imag. 30 606

    [160]
    [161]

    Lu X, Sun Y, Yuan Y 2011 Neurocomputing 74 661

    [162]

    Lu X, Sun Y, Yuan Y 2011 Pattern Recogn. 44 2427

    [163]
    [164]
    [165]

    Han X, Bian J, Ritman E J, Sidky E Y, Pan X 2012 Phys. Med. Biol. 57 5245

    [166]

    Liu Y, Ma J H, Fan Y, Liang Z 2012 Phys. Med. Biol. 57 7923

    [167]
    [168]

    Yu W, Zeng L, Liu B 2013 J. Electron. Imaging 22 033015

    [169]
    [170]
    [171]

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

    [172]

    Li C 2009 M.S. Dissertation (Houston: Rice University)

    [173]
    [174]
    [175]

    Osher S, Yin W, Goldfarb D 2008 SIAM J. Imag. Sci. 1 143

    [176]
    [177]

    Esser E 2009 UCLA CAM Tech. Rep. 2009-31

    [178]
    [179]

    Vandeghinste B, Goossens B, De Beenhouwer J, Pizurica A, Philips W, Vandenberghe S, Staelens S 2011 Proceedings of 11th International Conference on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine Potsdam, Germany, July 11-15, 2011 p431

    [180]
    [181]

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

    [182]
    [183]

    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]

    [184]
    [185]

    He B, Liao L, Han D, Yang H 2002 Math. Program. 92 103

    [186]

    Xiao Y, Yang J, Yuan X 2012 Inverse Prob. Imag. 6 547

    [187]
    [188]

    Xiao Y, Song H 2012 J. Math. Imaging Vis. 44 114

    [189]
    [190]

    Cai A, Wang L, Zhang H, Yan B, Li J, Li L, Xi X J. X-ray Sci. Technol. 22 335

    [191]
    [192]

    Chen C, Xu G 2013 UCLA CAM Tech. Rep 2013-66

    [193]
    [194]

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

    [195]
    [196]
    [197]

    Sidky E Y, Jrgensen J H, Pan X 2012 Phys. Med. Biol. 57 3065

    [198]

    Chambolle A, Pock T 2011 J. Math. Imaging Vis. 40 1

    [199]
    [200]

    Chang M, Li L, Chen Z, Xiao Y, Zhang L, Wang G 2013 J. X-ray Sci. Technol. 21 161

    [201]
    [202]
    [203]

    Chen G, Tang J, Leng S 2008 Med. Phys. 35 660

    [204]

    Chen G, Tang J, Hsieh J 2009 Med. Phys. 36 2130

    [205]
    [206]
    [207]

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

    [208]
    [209]

    Huang J, Zhang Y, Ma J, Zeng D, Bian Z, Niu S, Feng Q, Liang Z, Chen W 2013 PLoS ONE 8 e79709

    [210]
    [211]

    Yu H, Wang G 2009 Phys. Med. Biol. 54 2791

    [212]

    Yu H, Yang J, Jiang M, Wang G 2009 Phys. Med. Biol. 54 N425

    [213]
    [214]
    [215]

    Yang J, Yu H, Jiang M, Wang G 2010 Inverse Prob. 26 035013

    [216]
    [217]

    Do S, Karl W C, Kalra M K, Brady T J, Pien H 2010 SPIE Proceeding Medical Imaging 2010: Physics of Medical Imaging San Diego, USA, February 13-18, 2010 p76225D

    [218]

    Debatin M, Stsepankou D, Hesser J 2013 Proceeding of the 12th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine California, USA, June 16-21, 2013 p134

    [219]
    [220]
    [221]

    Xu Q, Yu H, Mou X, Wang G 2011 Proceeding of the 11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine Postdam, Germany, July 11-15, 2011 p258

    [222]

    Niu S, Gao Y, Bian Z, Huang J, Chen W, Yu G, Liang Z, Ma J 2014 Phys. Med. Biol. 59 2997

    [223]
    [224]

    Xu Q, Yu H, Mou X, Zhang L, Hsieh J, Wang G 2012 IEEE Trans. Med. Imag. 31 1682

    [225]
    [226]

    Lu Y, Zhao J, Wang G 2012 Phys. Med. Biol. 57 173

    [227]
    [228]

    Zhao B, Ding H, Lu Y, Wang G, Zhao J, Molloi S 2012 Phys. Med. Biol. 57 8217

    [229]
    [230]

    Zhao K, Pan J X, Kong H H 2013 Proccedings of 13th Chinese National Symposium for Stereology and Image Analysis Taiyuan, China, Semptember 23-25, 2013 p422 (in Chinese) [赵可, 潘晋孝, 孔慧华 2013 第十三届中国体视觉与图像分析学术会议论文集, 太原, 中国, 2013年9月23--25日第422页

    [231]
    [232]
    [233]
    [234]

    Jrgensen J S, Sidky E Y, Pan X 2013 IEEE Trans. Med. Imag. 32 460

    [235]
    [236]
    [237]
    [238]

    Elad M 2012 IEEE Sig. Proc. Lett. 19 922

    [239]
    [240]

    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]

    [241]
    [242]

    Wang L, Cai A, Zhang H, Yan B, Li L, Hu G 2013 Comput. Math. Methods. Med. 2013 418747

    [243]
    [244]

    Strohmer T 2012 IEEE Sig. Proc. Lett. 19 887

  • [1]

    Pan X, Sidky E Y, Vannier M 2009 Inverse Prob. 25 123009

    [2]

    Xu Q 2012 Ph. D. Dissertation (Xi'an: Xi'an Jiaotong University) (in Chinese) [许琼 2012 博士学位论文 (西安: 西安交通大学)]

    [3]
    [4]
    [5]

    Tuy H 1983 SIAM J. Appl. Math. 43 546

    [6]

    Smith B D 1985 IEEE Trans. Med. Imag. 4 14

    [7]
    [8]

    Heffernan P B, Robb R A 1983 IEEE Trans. Biomed. Eng. 30 838

    [9]
    [10]
    [11]

    Sezan M I, Stark H 1984 IEEE Trans. Med. Imag. 3 91

    [12]
    [13]

    Reis M L, Roberty N C 1992 Inverse Prob. 8 623

    [14]

    La Riviere P J, Pan X 1999 SPIE Proceeding Medical Imaging 1999: Physics of Medical Imaging San Diego, USA, February 20-26, 1999 p398

    [15]
    [16]

    Zhong Z G, Mei Y C, Wang Y P 1992 J. Wuhan Univ. (Nat. Sci. Ed.) 38 48 (in Chinese) [钟志刚, 梅雁诚, 王延平 1992 武汉大学学报(自然科学版) 38 48]

    [17]
    [18]

    L H, Li S G, Xu W Z, Yan X, L Y 1997 J. Chongqing Univ. 20 41 (in Chinese) [吕红, 李时光, 徐问之, 闫旭, 吕怡 1997 重庆大学学报 20 41]

    [19]
    [20]
    [21]

    Duan X H, Zhang L, Chen Z Q, Cheng J P 2007 Computerized Tomography Theory and Applications 16 1 (in Chinese) [段新辉, 张丽, 陈志强, 程建平 2007 CT理论与应用研究 16 1]

    [22]
    [23]

    Que J M, Wang Y F, Sun C L, Wei C F, Shi R J, Wei L 2012 Computerized Tomography Theory and Applications 21 169 (in Chinese) [阙介民, 王燕芳, 孙翠丽, 魏存峰, 史戎坚, 魏龙 2012 CT理论与应用研究 21 169]

    [24]

    Hunink M G M, Gazelle G S 2003 J. Clin. Invest. 111 1612

    [25]
    [26]
    [27]

    Imhof H, Schibany N, Ba-Ssalamah A, Czerny C, Hojreh A, Kainberger F, Krestan C, Kudler H, Nbauer I, Nowotny R 2003 Eur. J. Radiol. 47 29

    [28]

    Liu Y, Zhang H 2008 Chin. J. Med. Imaging Technol. 24 17 (in Chinese) [刘勇, 张华 2008 中国医学影像技术 24 17]

    [29]
    [30]

    Wang L Y 2010 M. S. Dissertation (Zhengzhou: PLA Information Engineering University) (in Chinese) [王林元 2010 硕士学位论文 (郑州: 解放军信息工程大学)]

    [31]
    [32]
    [33]

    Guo W 2011 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [郭威 2011 博士学位论文 (长春: 吉林大学)]

    [34]
    [35]

    Guo Q 2008 M. S. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [郭琦 2008 硕士学位论文 (合肥: 中国科学技术大学)]

    [36]

    Hu X Z 2008 M. S. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [胡小舟 2008 硕士学位论文 (合肥: 中国科学技术大学)]

    [37]
    [38]

    Kouris K, Tuy H, Lent A, Herman G T, Lewitt R M 1982 IEEE Trans. Med. Imag. 1 161

    [39]
    [40]

    Sidky E Y, Kao C M, Pan X 2006 J. X-ray Sci. Technol. 14 119

    [41]
    [42]
    [43]

    Liu N 2011 M. S. Dissertation (Guangzhou: Southern Medical University) (in Chinese) [刘楠 2011 硕士学位论文 (广州: 南方医科大学)]

    [44]
    [45]

    Liu W L 2013 M. S. Dissertation (Xi'an: Fourth Military Medical University) (in Chinese) [刘文磊 2013 硕士学位论文 (西安: 第四军医大学)]

    [46]
    [47]

    Inouye T 1979 IEEE Trans. Nucl. Sci. 26 2666

    [48]
    [49]

    Tam K C, Perez-Mendes V 1981 J. Opt. Soc. Am. 71 582

    [50]
    [51]

    Andersen A H 1989 IEEE Trans. Med. Imag. 8 50

    [52]
    [53]

    Gao H W, Zhang L, Chen Z Q, Cheng J P 2006 Computerized Tomography Theory and Applications 15 46 (in Chinese) [高河伟, 张丽, 陈志强, 程建平 2006 CT理论与应用研究15 46]

    [54]

    Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2009 Computerized Tomography Theory and Applications 18 22 (in Chinese) [王林元, 李磊, 闫镔, 江成顺, 王浩宇, 包尚联 2009 CT理论与应用研究 18 22]

    [55]
    [56]

    Jiao L C, Yang S Y, Liu F, Hou B 2011 Acta Electron. Sin. 39 1651 (in Chinese) [焦李成, 杨淑媛, 刘芳, 侯彪 2011 电子学报 39 1651]

    [57]
    [58]

    Wen Z W, Yin W T, Liu X, Zhang Y 2012 Oper. Res. Trans. 16 49 (in Chinese) [文再文, 印卧涛, 刘歆, 张寅 2012 运筹学学报 16 49]

    [59]
    [60]
    [61]

    Donoho D L 2006 Commun. Pure Appl. Math. 59 797

    [62]
    [63]

    Natarajin B K 1995 SIAM J. Comput. 24 227

    [64]

    Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289

    [65]
    [66]
    [67]

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

    [68]

    Candes E J, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [69]
    [70]
    [71]

    Donoho D L, Elad M 2003 Proc. Nat. Acad. Sci. USA 100 2197

    [72]
    [73]

    Gribonval R, Nielsen M 2003 IEEE Trans. Inf. Theory 49 3320

    [74]

    Zhang Y 2008 Rice University CAAM Tech. Rep. 2008-11

    [75]
    [76]

    Candes E J, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [77]
    [78]

    Candes E J 2008 CR Math. 346 589

    [79]
    [80]
    [81]

    Blanchard J, Cartis C, Tanner J 2009 IEEE Sig. Proc. Lett. 16 572

    [82]

    Candes E J 2007 IEEE Signal Proc. Mag. 24 21

    [83]
    [84]
    [85]
    [86]

    Figueiredo M, Nowak R, Wright S 2007 IEEE J. Sel. Top. Signal Process. 1 586

    [87]
    [88]

    Hale E, Yin W, Zhang Y 2008 SIAM J. Optimiz. 19 1107

    [89]
    [90]

    Hale E, Yin W, Zhang Y 2010 J. Comput. Math. 28 170

    [91]

    Wright S J, Nowak R D, Figueiredo M A T 2009 IEEE Trans. Sig. Proc. 57 2479

    [92]
    [93]
    [94]

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

    [95]

    Yun S, Toh K 2011 Comput. Optim. Appl. 48 273

    [96]
    [97]
    [98]

    Friedlander M, Vandenberg E 2008 SIAM J. Sci. Comput. 31 890

    [99]
    [100]

    Becker S, Bobin J, Candes E J 2011 SIAM J. Imag. Sci. 4 1

    [101]

    Yang J, Zhang Y 2011 SIAM J. Sci. Comput. 33 250

    [102]
    [103]
    [104]

    Deng W, Yin W, Zhang Y 2011 Rice University CAAM Tech. Rep. 2011-06

    [105]

    Gabay D, Mercier B 1976 Comput. Math. Appl. 2 17

    [106]
    [107]

    Hager W W, Hearn D W, Pardalos P M 1993 Large Scale Optimization: State of the Art (California: Springer US Press) p119

    [108]
    [109]
    [110]

    Chen G, Teboulle M 1994 Math. Program. 64 81

    [111]

    Wang Y, Yin W 2010 SIAM J. Imag. Sci. 3 856

    [112]
    [113]

    Li C, Yin W, Jiang H, Zhang Y 2012 Rice University CAAM Tech. Rep. 2012-13

    [114]
    [115]
    [116]

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

    [117]
    [118]
    [119]

    Parikh N, Boyd S 2014 Math. Prog. Comp. 6 77

    [120]
    [121]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 IEEE Trans. Sig. Proc. 60 1942

    [122]
    [123]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, March 25-30, 2012 p2869

    [124]
    [125]
    [126]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2013 IEEE Trans. Sig. Proc. 61 2718

    [127]
    [128]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of 51st IEEE Conference on Decision and Control (CDC) Hawaiian Islands, USA, December 10-13, 2012 p5116

    [129]
    [130]

    Mota J F C, Xavier J M F, Aguiar P M Q, Pschel M 2012 Proceedings of 51st IEEE Conference on Decision and Control (CDC) Hawaiian Islands, USA, December 10-13, 2012 p5110

    [131]
    [132]
    [133]

    Deng W, Yin W 2012 Rice University CAAM Tech. Rep. 2012-14

    [134]
    [135]
    [136]

    Shi W, Ling Q, Yuan K, Wu G, Yin W 2013 Proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP) Vancouver, Canada, May 26-31, 2013 p4613

    [137]
    [138]
    [139]

    Deng W, Lai M, Yin W 2013 UCLA CAM Tech. Rep. 2013-64

    [140]
    [141]

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

    [142]
    [143]

    Jin X, Li L, Chen Z, Zhang L, Xing Y 2010 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, Knoxville, USA, October 30- November 6, 2010 p2232

    [144]
    [145]

    Xu Q, Mou X, Tang S, Zhang Y 2010 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference Knoxville, USA, October 30-November 6, 2010 p3241

    [146]
    [147]

    Debatin M, Zygmanski P, Stsepankou D, Hesser J 2012 Proceddings of the IEEE Nuclear Science Symposium and Medical Imaging Conference Anaheim, USA, October 27-November 3, 2012 p2295

    [148]

    Chen Z, Jin X, Li L, Wang G 2013 Phys. Med. Biol. 58 2119

    [149]
    [150]
    [151]

    Lian Q S, Hao P P 2009 Opt. Tech. 35 422 (in Chinese) [练秋生, 郝鹏鹏 2009 光学技术 35 422]

    [152]
    [153]

    Zou J, Sun Y Q, Zhang P 2009 Acta Opt. Sin. 29 1198 (in Chinese) [邹晶, 孙艳勤, 张朋 2009 光学学报 29 1198]

    [154]

    Yu H, Wang G 2010 Phys. Med. Biol. 55 3905

    [155]
    [156]

    Bian J, Siewerdsen J H, Han X, Sidky E Y, Prince J L, Pelizzari C A, Pan X 2010 Phys. Med. Biol. 55 6575

    [157]
    [158]
    [159]

    Han X, Bian J, Eaker D R, Kline T L, Sidky E Y, Ritman E L, Pan X 2011 IEEE Trans. Med. Imag. 30 606

    [160]
    [161]

    Lu X, Sun Y, Yuan Y 2011 Neurocomputing 74 661

    [162]

    Lu X, Sun Y, Yuan Y 2011 Pattern Recogn. 44 2427

    [163]
    [164]
    [165]

    Han X, Bian J, Ritman E J, Sidky E Y, Pan X 2012 Phys. Med. Biol. 57 5245

    [166]

    Liu Y, Ma J H, Fan Y, Liang Z 2012 Phys. Med. Biol. 57 7923

    [167]
    [168]

    Yu W, Zeng L, Liu B 2013 J. Electron. Imaging 22 033015

    [169]
    [170]
    [171]

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

    [172]

    Li C 2009 M.S. Dissertation (Houston: Rice University)

    [173]
    [174]
    [175]

    Osher S, Yin W, Goldfarb D 2008 SIAM J. Imag. Sci. 1 143

    [176]
    [177]

    Esser E 2009 UCLA CAM Tech. Rep. 2009-31

    [178]
    [179]

    Vandeghinste B, Goossens B, De Beenhouwer J, Pizurica A, Philips W, Vandenberghe S, Staelens S 2011 Proceedings of 11th International Conference on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine Potsdam, Germany, July 11-15, 2011 p431

    [180]
    [181]

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

    [182]
    [183]

    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]

    [184]
    [185]

    He B, Liao L, Han D, Yang H 2002 Math. Program. 92 103

    [186]

    Xiao Y, Yang J, Yuan X 2012 Inverse Prob. Imag. 6 547

    [187]
    [188]

    Xiao Y, Song H 2012 J. Math. Imaging Vis. 44 114

    [189]
    [190]

    Cai A, Wang L, Zhang H, Yan B, Li J, Li L, Xi X J. X-ray Sci. Technol. 22 335

    [191]
    [192]

    Chen C, Xu G 2013 UCLA CAM Tech. Rep 2013-66

    [193]
    [194]

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

    [195]
    [196]
    [197]

    Sidky E Y, Jrgensen J H, Pan X 2012 Phys. Med. Biol. 57 3065

    [198]

    Chambolle A, Pock T 2011 J. Math. Imaging Vis. 40 1

    [199]
    [200]

    Chang M, Li L, Chen Z, Xiao Y, Zhang L, Wang G 2013 J. X-ray Sci. Technol. 21 161

    [201]
    [202]
    [203]

    Chen G, Tang J, Leng S 2008 Med. Phys. 35 660

    [204]

    Chen G, Tang J, Hsieh J 2009 Med. Phys. 36 2130

    [205]
    [206]
    [207]

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

    [208]
    [209]

    Huang J, Zhang Y, Ma J, Zeng D, Bian Z, Niu S, Feng Q, Liang Z, Chen W 2013 PLoS ONE 8 e79709

    [210]
    [211]

    Yu H, Wang G 2009 Phys. Med. Biol. 54 2791

    [212]

    Yu H, Yang J, Jiang M, Wang G 2009 Phys. Med. Biol. 54 N425

    [213]
    [214]
    [215]

    Yang J, Yu H, Jiang M, Wang G 2010 Inverse Prob. 26 035013

    [216]
    [217]

    Do S, Karl W C, Kalra M K, Brady T J, Pien H 2010 SPIE Proceeding Medical Imaging 2010: Physics of Medical Imaging San Diego, USA, February 13-18, 2010 p76225D

    [218]

    Debatin M, Stsepankou D, Hesser J 2013 Proceeding of the 12th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine California, USA, June 16-21, 2013 p134

    [219]
    [220]
    [221]

    Xu Q, Yu H, Mou X, Wang G 2011 Proceeding of the 11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine Postdam, Germany, July 11-15, 2011 p258

    [222]

    Niu S, Gao Y, Bian Z, Huang J, Chen W, Yu G, Liang Z, Ma J 2014 Phys. Med. Biol. 59 2997

    [223]
    [224]

    Xu Q, Yu H, Mou X, Zhang L, Hsieh J, Wang G 2012 IEEE Trans. Med. Imag. 31 1682

    [225]
    [226]

    Lu Y, Zhao J, Wang G 2012 Phys. Med. Biol. 57 173

    [227]
    [228]

    Zhao B, Ding H, Lu Y, Wang G, Zhao J, Molloi S 2012 Phys. Med. Biol. 57 8217

    [229]
    [230]

    Zhao K, Pan J X, Kong H H 2013 Proccedings of 13th Chinese National Symposium for Stereology and Image Analysis Taiyuan, China, Semptember 23-25, 2013 p422 (in Chinese) [赵可, 潘晋孝, 孔慧华 2013 第十三届中国体视觉与图像分析学术会议论文集, 太原, 中国, 2013年9月23--25日第422页

    [231]
    [232]
    [233]
    [234]

    Jrgensen J S, Sidky E Y, Pan X 2013 IEEE Trans. Med. Imag. 32 460

    [235]
    [236]
    [237]
    [238]

    Elad M 2012 IEEE Sig. Proc. Lett. 19 922

    [239]
    [240]

    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]

    [241]
    [242]

    Wang L, Cai A, Zhang H, Yan B, Li L, Hu G 2013 Comput. Math. Methods. Med. 2013 418747

    [243]
    [244]

    Strohmer T 2012 IEEE Sig. Proc. Lett. 19 887

计量
  • 文章访问数:  6473
  • PDF下载量:  1733
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-03-22
  • 修回日期:  2014-06-19
  • 刊出日期:  2014-10-05

/

返回文章
返回