Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(7): 078701    DOI: 10.1088/1674-1056/25/7/078701

Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity

Han-Ming Zhang(张瀚铭), Lin-Yuan Wang(王林元), Lei Li(李磊), Bin Yan(闫镔), Ai-Long Cai(蔡爱龙), Guo-En Hu(胡国恩)
National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China
Abstract  The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography (CT) reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts. To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated. The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.
Keywords:  computed tomography      image reconstruction      sparsity exploitation      nonlocal gradient  
Received:  29 December 2015      Revised:  26 February 2016      Published:  05 July 2016
PACS:  87.59.-e (X-ray imaging)  
  07.85.-m (X- and γ-ray instruments)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61372172).
Corresponding Authors:  Bin Yan     E-mail:

Cite this article: 

Han-Ming Zhang(张瀚铭), Lin-Yuan Wang(王林元), Lei Li(李磊), Bin Yan(闫镔), Ai-Long Cai(蔡爱龙), Guo-En Hu(胡国恩) Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity 2016 Chin. Phys. B 25 078701

[1] Fazel R, Krumholz H M, Wang Y, et al. 2009 New Engl. J. Med. 361 849
[2] Brenner D J and Hall E J 2007 New Engl. J. Med. 357 2277
[3] Wang J, Liang Z, Lu H and Xing L 2010 Curr. Med. Imaging Rev. 6 72
[4] Sidky E Y, Kao C M and Pan X C 2006 J. X-Ray Sci. Technol. 14 119
[5] Gordon R, Bender R and Herman G T 1970 J. Theor. Biol. 29 471
[6] Andersen A and Kak A 1984 Ultrasonic Imaging 6 81
[7] Lange K and Carson R 1984 J. Comput. Assist. Tomo. 8 306
[8] Sidky E Y and Pan X C 2008 Phys. Med. Biol. 17 4777
[9] Han X, Bian J G, Eaker D R, Kline T L, Sidky E Y, Ritman E L and Pan X C 2011 IEEE Trans. Med. Imag. 30 606
[10] Han X, Bian J G, Ritman E L, Sidky E Y and Pan X C 2012 Phys. Med. Biol. 57 5245
[11] Duan X H, Cheng J P, Zhang L, Xing Y X, Chen Z Q and Zhao Z R 2009 IEEE Trans. Nucl. Sci. 56 1377
[12] Chen Z Q, Jin X, Li L and Wang G 2013 Phys. Med. Biol. 58 2119
[13] Wang L Y, Zhang H M, Cai A L, Yan B, Li L and Hu G E 2013 Acta Phys. Sin. 62 198701 (in Chinese)
[14] Bian J G, Siewerdsen J H, Han X, Sidky E Y, Prince J L, Pelizzari C A and Pan X C 2010 Phys. Med. Biol. 22 6575
[15] Tang J, Nett B E and Chen G 2009 Phys. Med. Biol. 54 5781
[16] Tian Z, Jia X, Yuan K H, Pan T and Jiang S B 2011 Phys. Med. Biol. 56 5949
[17] Liu Y, Ma J, Fan Y and Liang Z 2012 Phys. Med. Biol. 57 7923
[18] Liu Y, Liang Z L, Ma J H, Lu H B, Wang K, Zhang H and Moore W 2014 IEEE Trans. Med. Imag. 33 749
[19] Cai A L, Wang L Y, Zhang H M, Yan B, Li L, Xi X Q and Li J X 2014 J. X-ray Sci. Technol. 22 335
[20] Niu S Z, Gao Y, Bian Z Y, Huang J, Chen W F, Yu G H, Liang Z R and Ma J H 2014 Phys. Med. Biol. 59 2997
[21] Buades A, Coll B and Morel J M 2005 Multiscale Model Simul. 4 490
[22] Gilboa G and Osher S 2007 Multiscale Model Simul. 6 595
[23] Gilboa G and Osher S 2007 Multiscale Model Simul. 7 1005
[24] Zhang X Q, Burger M, Bresson X and Osher S 2010 SIAM J. Imaging Sci. 3 253
[25] Lou Y F, Zhang X Q, Osher S and Bertozzi A 2010 Journal of Scientific Computing 42 185
[26] Zhang Y, Zhang W H and Zhou J L 2014 The Scientific World Journal 2014 458496
[27] Wang Y L, Yang J F, Yin W T and Zhang Y 2008 SIAM J. Imaging Sci. 1 248
[28] Zhang H M, Wang L Y, Yan B, Li L, Xi X Q and Lu L Z 2013 Chin. Phys. B 22 078701
[29] Zhang H M, Wang L Y, Yan B, Li L, Cai A L and Hu G E 2016 PLoS ONE 11 e0149899
[30] Li C, Yin W, Jiang H and Zhang Y 2013 Comput. Optim. Appl. 56 507
[31] Xu H Y, Sun Q S, Luo N, Cao G and Xia D 2013 PLoS ONE 8 e65865
[32] Zelnik-Manor L and Perona P 2004 Advances in Neural Information Processing Systems, December 13-18, 2004, Vancouver, Canada, p. 1601
[33] Smith D S and Welch E B 2011 Proceedings of 19th Annual Meeting of International Society for Magnetic Resonance in Medicine, May 7-13, 2011, Montreal, Canada, p. 2845
[34] Chen J L, Li L, Wang L Y, Cai A L, Xi X Q, Zhang H M, Li J X and Yan B 2015 Chin. Phys. B 24 028703
[1] High-resolution bone microstructure imaging based on ultrasonic frequency-domain full-waveform inversion
Yifang Li(李义方), Qinzhen Shi(石勤振), Ying Li(李颖), Xiaojun Song(宋小军), Chengcheng Liu(刘成成), Dean Ta(他得安), and Weiqi Wang(王威琪). Chin. Phys. B, 2021, 30(1): 014302.
[2] Terahertz two-pixel imaging based on complementary compressive sensing
Yuye Wang(王与烨), Yuchen Ren(任宇琛), Linyu Chen(陈霖宇), Ci Song(宋词), Changzhao Li(李长昭), Chao Zhang(张超), Degang Xu(徐德刚), Jianquan Yao(姚建铨). Chin. Phys. B, 2018, 27(11): 114204.
[3] Image reconstruction for cone-beam computed tomography using total p-variation plus Kullback–Leibler data divergence
Ai-Long Cai(蔡爱龙), Lei Li(李磊), Lin-Yuan Wang(王林元), Bin Yan(闫镔), Zhi-Zhong Zheng(郑治中), Han-Ming Zhang(张瀚铭), Guo-En Hu(胡国恩). Chin. Phys. B, 2017, 26(7): 078701.
[4] Sub-Rayleigh imaging via undersampling scanning based on sparsity constraints
Chang-Bin Xue(薛长斌), Xu-Ri Yao(姚旭日), Long-Zhen Li(李龙珍), Xue-Feng Liu(刘雪峰), Wen-Kai Yu(俞文凯), Xiao-Yong Guo(郭晓勇), Guang-Jie Zhai(翟光杰), Qing Zhao(赵清). Chin. Phys. B, 2017, 26(2): 024203.
[5] Single-shot grating-based x-ray differential phase contrast imaging with a modified analyzer grating
Chen-Xi Wei(卫晨希), Zhao Wu(吴朝), Faiz Wali, Wen-Bin Wei(魏文彬), Yuan Bao(鲍园), Rong-Hui Luo(骆荣辉), Lei Wang(王磊), Gang Liu(刘刚), Yang-Chao Tian(田扬超). Chin. Phys. B, 2017, 26(10): 108701.
[6] Cosine fitting radiography and computed tomography
Li Pan-Yun, Zhang Kai, Huang Wan-Xia, Yuan Qing-Xi, Wang Yan, Ju Zai-Qiang, Wu Zi-Yu, Zhu Pei-Ping. Chin. Phys. B, 2015, 24(6): 068704.
[7] Fast parallel algorithm for three-dimensional distance-driven model in iterative computed tomography reconstruction
Chen Jian-Lin, Li Lei, Wang Lin-Yuan, Cai Ai-Long, Xi Xiao-Qi, Zhang Han-Ming, Li Jian-Xin, Yan Bin. Chin. Phys. B, 2015, 24(2): 028703.
[8] Pulse decomposition-based analysis of PAT/TAT error caused by negative lobes in limited-view conditions
Liu Liang-Bing, Tao Chao, Liu Xiao-Jun, Li Xian-Li, Zhang Hai-Tao. Chin. Phys. B, 2015, 24(2): 024304.
[9] Enhancement of photoacoustic tomography in the tissue with speed-of-sound variance using ultrasound computed tomography
Cheng Ren-Xiang, Tao Chao, Liu Xiao-Jun. Chin. Phys. B, 2015, 24(11): 114301.
[10] Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method
Bao Yuan, Wang Yan, Gao Kun, Wang Zhi-Li, Zhu Pei-Ping, Wu Zi-Yu. Chin. Phys. B, 2015, 24(10): 108702.
[11] Scatter correction method for cone-beam CT based on interlacing-slit scan
Huang Kui-Dong, Zhang Hua, Shi Yi-Kai, Zhang Liang, Xu Zhe. Chin. Phys. B, 2014, 23(9): 098106.
[12] Formation of multifunctional Fe3O4/Au composite nanoparticles for dual-mode MR/CT imaging applications
Hu Yong, Li Jing-Chao, Shen Ming-Wu, Shi Xiang-Yang. Chin. Phys. B, 2014, 23(7): 078704.
[13] Penetrating view of nano-structures in Aleochara verna spermatheca and flagellum by hard X-ray microscopy
Zhang Kai, Li Dee, Hong You-Li, Zhu Pei-Ping, Yuan Qing-Xi, Huang Wan-Xia, Gao Kun, Zhou Hong-Zhang, Wu Zi-Yu. Chin. Phys. B, 2013, 22(7): 076801.
[14] Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography
Zhang Han-Ming, Wang Lin-Yuan, Yan Bin, Li Lei, Xi Xiao-Qi, Lu Li-Zhong. Chin. Phys. B, 2013, 22(7): 078701.
[15] Multiple helical scans and the reconstruction of over FOV-sized objects in cone-beam CT
Han Yu, Yan Bin, Li Lei, Yu Chao-Qun, Li Jian-Xin, Bao Shang-Lian. Chin. Phys. B, 2012, 21(6): 068701.
No Suggested Reading articles found!