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康普顿散射成像技术利用射线与物质作用后的散射光子信息对物质的电子密度进行成像. 与传统的透射成像方式相比，康普顿散射成像具有系统结构灵活、成像对比度高、辐射剂量低等优势，在无损检测、医疗诊断、安全检查等领域有着广阔的应用前景. 但其重建问题是一个非线性的逆问题，通常是不适定的，其解对噪声和测量误差非常敏感. 为解决此问题，本文结合全变分最小化正则化方法和交替方向法提出了一种新的康普顿散射成像重建算法. 该算法首先将问题对应的TV模型转化为与之等价的带约束的优化问题，然后利用增广拉格朗日乘子法将优化问题分解为两个具有解析解的子问题，并通过交替求解子问题使增广拉格朗日函数达到最小，进而得到重建的图像. 在仿真实验中，通过与主流的ASD-POCS方法进行对比，证明了该算法在重建精度和重建效率方面的优势.Compton scatter tomography measures samples electron densities utilizing the scattered photons. Compared to traditional transmission imaging models, Compton scatter tomography has the following characteristics, i.e. freedom in construction systems, greater sensitivity for low-density materials, and lower radiation dose. It has been applied in non-destructive testing, medical, and security inspections, and other fields. However, Compton scatter tomography reconstruction is a nonlinear inverse problem, common is ill-posed, and its solutions are very sensitive to noise and erroneous measurements. To tackle the problem, in this paper we propose a novel Compton scatter tomography reconstruction algorithm based on the total variation minimization and alternating direction method. The main idea of our method is to reformulate the reconstruction problems TV function as an optimization with constrains where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method to solve the sub-problems. Numerical experiments shows that the reconstruction quality and efficiency of the proposed method are improved compared to the adaptive-steepest-descent-projection onto convex sets method.
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Keywords:
- Compton scatter tomography /
- image reconstruction /
- total variation minimization /
- alternating direction method
[1] Tang S S, Hussein E M A 2004 Appl. Radiat.Isot. 61 3
[2] Hussein E M A, Desrosiers M, Waller E J 2005 Radiat. Phys. Chem. 73 7
[3] Evans B L, Martin J B, Burggraf L W, Roggemann M C, Hangartner T N 2002 Nuclear Instruments and Methods in Physics Research A 480 797
[4] Harding G, Harding E 2010 Appl. Radiat. Isot. 68 993
[5] Harding G 2004 Radiat. Phys. Chem. 71 869
[6] Faysal E K, Ilan Y, Hussein E M A 2003 Phys. Med. Biol. 48 3445
[7] Pistolesi M, Miniati M 1981 Nucl. Med. All. Sci. 25 182
[8] Shin W P, Sunwoo Y, Jun S R 2006 Nuclear Instruments and Methods 568 369
[9] Michael D H, Joseph J M, Dennis G L, Gary L C 1994 IEEE T. Med. Imaging 13 461
[10] Lale P G 1959 Phys. Med. Biol. 18 532
[11] Wang J J, Huang X W, Zhong X R 2004 Chinese Journal of Scientific Instrument 25 164 (in Chinese) [王加俊, 黄贤武, 仲兴荣 2004 仪器仪表学 25 164]
[12] Truong T T, Nguyen M K 2011 Inverse Problems 27 1
[13] Farmer F T, Collins M P 1971 Phys. Med. Bio. 16 577
[14] Kondic N N, Jacobs A M, Ebert D 1983 American Nuclear Society 2 1443
[15] Hussein E M, AMeneley D A, Banerjee S 1986 Nucl. Sci. Eng. 92 341
[16] Arendtsz N V, Hussein E M A 1995 IEEE Trans. Nucl. Sci. 42 2155
[17] Wang J J, Huang X W, Zhao R 2004 Microelectronics & Computer 21 95 (in Chinese) [王加俊, 黄贤武, 赵然 2004 微电子学与计算机 21 95]
[18] ArendtszN V, HusseinE M A 1993 SPIE Vol. 2035 Mathematical Methods in Medical Imaging Ⅱ San Diego, CA, July, 1993 p230
[19] Li S P, Wang L Y, Yan B, Li L, Liu Y J 2012 Chin. Phys. B 21 108703
[20] Candes E, Tao T 2006 IEEE Trans. Inf. Theory 52 5406
[21] Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489
[22] Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777
[23] Zhang H M, Wang L Y, Yan B, Li L, Xi X Q, Lu L Z 2013 Chin. Phys. B 22 078701
[24] Li C B 2009 MS Dissertation (Houston: Rice University)
[25] Wang Y L, Yang J F, Yin W T, Zhang Y 2008 SIAM J. Imag. Sci. 1 248
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[1] Tang S S, Hussein E M A 2004 Appl. Radiat.Isot. 61 3
[2] Hussein E M A, Desrosiers M, Waller E J 2005 Radiat. Phys. Chem. 73 7
[3] Evans B L, Martin J B, Burggraf L W, Roggemann M C, Hangartner T N 2002 Nuclear Instruments and Methods in Physics Research A 480 797
[4] Harding G, Harding E 2010 Appl. Radiat. Isot. 68 993
[5] Harding G 2004 Radiat. Phys. Chem. 71 869
[6] Faysal E K, Ilan Y, Hussein E M A 2003 Phys. Med. Biol. 48 3445
[7] Pistolesi M, Miniati M 1981 Nucl. Med. All. Sci. 25 182
[8] Shin W P, Sunwoo Y, Jun S R 2006 Nuclear Instruments and Methods 568 369
[9] Michael D H, Joseph J M, Dennis G L, Gary L C 1994 IEEE T. Med. Imaging 13 461
[10] Lale P G 1959 Phys. Med. Biol. 18 532
[11] Wang J J, Huang X W, Zhong X R 2004 Chinese Journal of Scientific Instrument 25 164 (in Chinese) [王加俊, 黄贤武, 仲兴荣 2004 仪器仪表学 25 164]
[12] Truong T T, Nguyen M K 2011 Inverse Problems 27 1
[13] Farmer F T, Collins M P 1971 Phys. Med. Bio. 16 577
[14] Kondic N N, Jacobs A M, Ebert D 1983 American Nuclear Society 2 1443
[15] Hussein E M, AMeneley D A, Banerjee S 1986 Nucl. Sci. Eng. 92 341
[16] Arendtsz N V, Hussein E M A 1995 IEEE Trans. Nucl. Sci. 42 2155
[17] Wang J J, Huang X W, Zhao R 2004 Microelectronics & Computer 21 95 (in Chinese) [王加俊, 黄贤武, 赵然 2004 微电子学与计算机 21 95]
[18] ArendtszN V, HusseinE M A 1993 SPIE Vol. 2035 Mathematical Methods in Medical Imaging Ⅱ San Diego, CA, July, 1993 p230
[19] Li S P, Wang L Y, Yan B, Li L, Liu Y J 2012 Chin. Phys. B 21 108703
[20] Candes E, Tao T 2006 IEEE Trans. Inf. Theory 52 5406
[21] Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489
[22] Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777
[23] Zhang H M, Wang L Y, Yan B, Li L, Xi X Q, Lu L Z 2013 Chin. Phys. B 22 078701
[24] Li C B 2009 MS Dissertation (Houston: Rice University)
[25] Wang Y L, Yang J F, Yin W T, Zhang Y 2008 SIAM J. Imag. Sci. 1 248
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