An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

doi:10.1088/1674-1056/24/10/104204

Abstract In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

Keywords: ill-posed problem emission tomography limited projections Tikhonov regularization

Received: 11 January 2015
Revised: 13 May 2015
Accepted manuscript online:

PACS:	42.30.Wb	(Image reconstruction; tomography)
	43.28.+h	(Aeroacoustics and atmospheric sound)

Fund: Project supported by the China National Funds for Distinguished Young Scientists of National Natural Science Foundation of China (Grant No. 51025622), the National Natural Science Foundation of China (Grant No. 51406095), and the 100 Top Talents Program of Tsinghua University, Beijing, China (2011).

Corresponding Authors: Zhou Huai-Chun
E-mail: hczh@mail.tsinghua.edu.cn

Cite this article:

Liu Hua-Wei (柳华蔚), Zheng Shu (郑树), Zhou Huai-Chun (周怀春) An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems 2015 Chin. Phys. B 24 104204

[1]	Lou C and Zhou H C 2005 Combust. Flame 143 97
[2]	Snelling D R, Thomson K A, Smallwood G J, Gülder Ö L, Weckman E J and Fraser R A 2002 AIAA J. 40 1789
[3]	Kimoto A, Nakatani T, Matsuoka Y I and Shida K 2005 IEEE Trans. Instrum. Meas. 54 2407
[4]	Yang F Q, Zhang D H, Huang K D, Wang K and Xue Z 2014 Acta Phys. Sin 63 058701 (in Chinese)
[5]	Wang Q and Wang H X 2011 ISA Trans. 50 256
[6]	Craciunescu T, Bonheure G, Kiptily V, Murari A, Tiseanu I, Zoita V and JET-EFDA Contributors 2009 Nucl. Instrum. Method Phys. Res. A 605 374.
[7]	Sidky E Y, Kao C M and Pan X C 2006 J. x-ray Sci. Technol. 14 119
[8]	Wang Q, Wand H X and Yan Y 2011 Flow Meas. Instrum. 22 295
[9]	Huang Q X, Wang F, Liu D, Ma Z Y, Yan J H, Chi Y and Cen K F 2009 Combust. Flame 156 5653
[10]	Ishino Y and Ohiwa N 2005 JSME Int. J. B 48 34
[11]	Balima O, Favennec Y and Rousse D 2013 J. Comput. Phys. 251 461
[12]	Zhu N, Jiang Y and Kato S 2005 Energy 30 509
[13]	Reis M L and Robery N C 1992 Inverse Probl. 8 623
[14]	Wei W D 1986 Acta Phys. Sin. 35 171 (in Chinese)
[15]	Li Y J, Liu Z and Yu H 2013 Acta Phys. Sin. 62 168902 (in Chinese)
[16]	Lin M B, Zhao C X, Yu X D, Yu F S, Yang T Y and Yan K 2014 Acta Phys. Sin. 63 138701 (in Chinese)
[17]	Gu Y F, Yan B, Li L, Wei F, Han Y and Chen J 2014 Acta Phys. Sin 63 058701 (in Chinese)
[18]	Fang S and Guo H 2014 Chin. Phys. B 23 057401
[19]	Zhao J, Xu Y B, Tan C and Dong F 2014 Meas. Sci. Technol. 25 085401
[20]	Yang D W, Xing D, X, Zhao X H, Pan C N and Fang J S 2010 Chin. Phys. Lett. 27 054301
[21]	Kim B S, Khambampati A K, Kim S and Kim K Y 2011 Meas. Sci. Technol. 22 104009
[22]	Zhou H C, Han S D, Sheng F and Zheng C G 2002 JQSRT 72 361
[23]	Liu H W, Lv W and Zhou H C 2013 IEEE Int. Conf. Imaging Systems and Techniques, October 22-23, 2013, Beijing, China, p. 321
[24]	Garda B and Galias Z 2012 Int. Conf. Signals and Electronic Systems, September 18-21, 2012, Wroclaw, Poland, p. 1
[25]	Chiao P, Fessler J A, Zasadny K R and Wahl R L 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference, October 21-28, 1995, San Francisco, CA, USA, p. 1680
[26]	Bro R and Jong S D 1997 J. Chemom. 11 393
[27]	Lu J 2009 "Study on measuring method of the temperature and soot volume fraction in laminar co-flow axisymmetric diffusion flames", Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)
[28]	Attivissimo F, Cavone G, Lanzolla A M L and Spadavecchia M 2005 IEEE Trans. Instrum. Meas. 59 125110.1109/TIM.2010.2040932"

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An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

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