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

doi:10.7498/aps.63.208702

Abstract

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.

Keywords:

Authors and contacts

1.
National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China;
2.
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116000, China
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).

References

[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

Cited By

[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]	Li Yong-Fei, Guo Rui-Ming, Zhao Hang-Fang. Sparse reconstruction of acoustic interference fringes in shallow water and internal wave environment. Acta Physica Sinica, 2023, 72(7): 074301. doi: 10.7498/aps.72.20221932
[2]	Li Ming-Fei, Yuan Zi-Hao, Liu Yuan-Xing, Deng Yi-Cheng, Wang Xue-Feng. Comparison between optimal configuration algorithms of fiber phased array. Acta Physica Sinica, 2021, 70(8): 084205. doi: 10.7498/aps.70.20201768
[3]	Zhong Ming-Yu, Xi Liang, Si Fu-Qi, Zhou Hai-Jin, Wang Yu. Tomographic reconstruction of stack plume based on sparse optimization. Acta Physica Sinica, 2019, 68(16): 164205. doi: 10.7498/aps.68.20190268
[4]	Qiao Zhi-Wei. The total variation constrained data divergence minimization model for image reconstruction and its Chambolle-Pock solving algorithm. Acta Physica Sinica, 2018, 67(19): 198701. doi: 10.7498/aps.67.20180839
[5]	Feng Hui, Sun Biao, Ma Shu-Gen. One-bit compressed sensing reconstruction for block sparse signals. Acta Physica Sinica, 2017, 66(18): 180202. doi: 10.7498/aps.66.180202
[6]	Qi Jun-Cheng, Chen Rong-Chang, Liu Bin, Chen Ping, Du Guo-Hao, Xiao Ti-Qiao. Grating based X-ray phase contrast CT imaging with iterative reconstruction algorithm. Acta Physica Sinica, 2017, 66(5): 054202. doi: 10.7498/aps.66.054202
[7]	Yang Jing, Wu Xue-Cheng, Wu Ying-Chun, Yao Long-Chao, Chen Ling-Hong, Qiu Kun-Zan, Cen Ke-Fa. Study on extending the depth of field in reconstructed image for a micro digital hologram. Acta Physica Sinica, 2015, 64(11): 114209. doi: 10.7498/aps.64.114209
[8]	Ma Ge, Hu Yue-Ming, Gao Hong-Xia, Li Zhi-Fu, Guo Qi-Wei. Physical total energy based objective function model for sparse reconstruction. Acta Physica Sinica, 2015, 64(20): 204202. doi: 10.7498/aps.64.204202
[9]	He Lin-Yang, Liu Jing-Hong, Li Gang. Super resolution of aerial image by means of polyphase components reconstruction. Acta Physica Sinica, 2015, 64(11): 114208. doi: 10.7498/aps.64.114208
[10]	Han Yu, Li Lei, Yan Bin, Xi Xiao-Qi, Hu Guo-En. A half-covered helical cone-beam reconstruction algorithm based on the Radon inversion transformation. Acta Physica Sinica, 2015, 64(5): 058704. doi: 10.7498/aps.64.058704
[11]	Mao Bao-Lin, Chen Xiao-Zhao, Xiao Da-Yu, Fan Sheng-Yu, Teng Yue-Yang, Kang Yan. Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy. Acta Physica Sinica, 2014, 63(13): 138701. doi: 10.7498/aps.63.138701
[12]	Deng Cheng-Zhi, Tian Wei, Chen Pan, Wang Sheng-Qian, Zhu Hua-Sheng, Hu Sai-Feng. Infrared image super-resolution via locality-constrained group sparse model. Acta Physica Sinica, 2014, 63(4): 044202. doi: 10.7498/aps.63.044202
[13]	Yang Fu-Qiang, Zhang Ding-Hua, Huang Kui-Dong, Wang Kun, Xu Zhe. Review of reconstruction algorithms with incomplete projection data of computed tomography. Acta Physica Sinica, 2014, 63(5): 058701. doi: 10.7498/aps.63.058701
[14]	Zhang Feng, Yan Bin, Wang Xian-Chao, Jiang Hua, Wei Xing. An efficient reconstruction algorithm for flat object based on backprojection filtration method in circular half-cover computed tomography. Acta Physica Sinica, 2013, 62(16): 168702. doi: 10.7498/aps.62.168702
[15]	Wang Xian-Chao, Yan Bin, Liu Hong-Kui, Li Lei, Wei Xing, Hu Guo-En. Efficient reconstruction from truncated data in circular cone-beam CT. Acta Physica Sinica, 2013, 62(9): 098702. doi: 10.7498/aps.62.098702
[16]	Ning Fang-Li, He Bi-Jing, Wei Juan. An algorithm for image reconstruction based on lp norm. Acta Physica Sinica, 2013, 62(17): 174212. doi: 10.7498/aps.62.174212
[17]	Wang Lin-Yuan, Zhang Han-Ming, Cai Ai-Long, Yan Bin, Li Lei, Hu Guo-En. Image reconstruction algorithm based on inexact alternating direction total-variation minimization. Acta Physica Sinica, 2013, 62(19): 198701. doi: 10.7498/aps.62.198701
[18]	Li Jun-Chang. Focal depth research of digital holographic reconstructed image. Acta Physica Sinica, 2012, 61(13): 134203. doi: 10.7498/aps.61.134203
[19]	Wang Ya-Qi, Jiang Guo-Ping. Virus spreading on complex networks with imperfect immunization. Acta Physica Sinica, 2010, 59(10): 6734-6743. doi: 10.7498/aps.59.6734
[20]	Zhang Kai, Zhu Pei-Ping, Huang Wan-Xia, Yuan Qing-Xi, Liu Li, Yuan Bin, Wang Jun-Yue, Shu Hang, Chen Bo, Liu Yi-Jin, Li En-Rong, Liu Xiao-Song, Wu Zi-Yu. The application of algebraic reconstruction techniques in X-ray refraction contrast CT. Acta Physica Sinica, 2008, 57(6): 3410-3418. doi: 10.7498/aps.57.3410

Catalog

Vol. 63, Issue 20 - 2014-10-20

Metrics

Abstract views: 8208
PDF Downloads: 1762
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板