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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

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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
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  • 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.
    • 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 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 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 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 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

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  • Abstract views:  8210
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  • Cited By: 0
Publishing process
  • Received Date:  22 March 2014
  • Accepted Date:  19 June 2014
  • Published Online:  05 October 2014

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