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The forward problem of diffuse optical tomography (DOT) is commonly solved by the finite element method (FEM) currently. However, with the increase of the model scale, the computational complexity of FEM increases significantly; while the boundary element method (BEM) attracts much attention because of its reduction in calculated dimensions. In this paper, the fast multipole boundary element method (FMBEM) for DOT is studied using a model of highly scattering homogenous medium. In FMBEM, by the multipole expansions of kernel functions, the product of matrix coefficient and iterative vector can be equivalent to the recursion of a quadtree; and then a generalized minimal residual method is used to solve the BEM equation iteratively. The calculations of the FMBEM are compared with Monte Carlo simulations. The results show that the calculations of the FMBEM are in good agreement with Monte Carlo simulations. This demonstrates the feasibility of FMBEM in DOT and indicates that the FMBEM has a bright future for large-scale and real-time imaging.
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Keywords:
- diffuse optical tomography /
- boundary element method /
- fast multipole boundary element method
[1] Stephanie M W Y, Van de ven S M, Elias S G 2009 Eur. Radiol. 19 1108
[2] Hebden J C, Austin T 2007 Eur. Radiol. 17 2926
[3] Deng Y, Zhang X X, Luo Z Y, Xu J, Yang X Q, Meng Y Z, Gong H, Luo Q M 2012 Acta Phys. Sin. 62 014202 (in Chinese) [邓勇, 张喧轩, 罗召洋, 许军, 杨孝全, 孟远征, 龚辉, 骆清铭 2012 62 014202]
[4] Srinivasan S, Ghadyani H R, Pogue B W, Paulsen K D 2009 Biomed. Opt. Express 1 398
[5] Elisee J P, Gibson A, Arridge S 2010 IEEE T. Bio-Med. Eng. 57 2737
[6] Elisee J P, Bonnet M, Arridge S 2011 Opt. Lett. 36 4101
[7] Li S D, Huang Q B, Li T Y 2012 Acta Phys. Sin. 61 064301 (in Chinese) [李善德, 黄其柏, 李天匀 2012 61 064301]
[8] Xu K X, Gao F, Zhao H J 2007 Biomedical Photonics (Beijing: Science Press) p53 (in Chinese) [徐可欣, 高峰, 赵会娟 2007 生物医学光子学 (北京: 科学出版社)第53页]
[9] Sikora J, Zacharopoulos A, Douiri A, Schweiger M, Horesh L, Arridge S, Ripoll J 2006 Phys. Med. Biol. 51 497
[10] LiuY J 2009 Fast Multipole Boundary Element Method (1st Ed.) (New York: Cambridge University Press) p157
[11] Yaoi Z H, Wang H T 2009 Boundary Element Methods (Beijing: Higher Education Press) p226 (in Chinese) [姚振汉, 王海涛 2009 边界元法(北京: 高等教育出版社)第226页]
[12] Wang H T, Yao Z H, Wang P B 2005 Eng. Anal. Bound. Elem. 29 673
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[1] Stephanie M W Y, Van de ven S M, Elias S G 2009 Eur. Radiol. 19 1108
[2] Hebden J C, Austin T 2007 Eur. Radiol. 17 2926
[3] Deng Y, Zhang X X, Luo Z Y, Xu J, Yang X Q, Meng Y Z, Gong H, Luo Q M 2012 Acta Phys. Sin. 62 014202 (in Chinese) [邓勇, 张喧轩, 罗召洋, 许军, 杨孝全, 孟远征, 龚辉, 骆清铭 2012 62 014202]
[4] Srinivasan S, Ghadyani H R, Pogue B W, Paulsen K D 2009 Biomed. Opt. Express 1 398
[5] Elisee J P, Gibson A, Arridge S 2010 IEEE T. Bio-Med. Eng. 57 2737
[6] Elisee J P, Bonnet M, Arridge S 2011 Opt. Lett. 36 4101
[7] Li S D, Huang Q B, Li T Y 2012 Acta Phys. Sin. 61 064301 (in Chinese) [李善德, 黄其柏, 李天匀 2012 61 064301]
[8] Xu K X, Gao F, Zhao H J 2007 Biomedical Photonics (Beijing: Science Press) p53 (in Chinese) [徐可欣, 高峰, 赵会娟 2007 生物医学光子学 (北京: 科学出版社)第53页]
[9] Sikora J, Zacharopoulos A, Douiri A, Schweiger M, Horesh L, Arridge S, Ripoll J 2006 Phys. Med. Biol. 51 497
[10] LiuY J 2009 Fast Multipole Boundary Element Method (1st Ed.) (New York: Cambridge University Press) p157
[11] Yaoi Z H, Wang H T 2009 Boundary Element Methods (Beijing: Higher Education Press) p226 (in Chinese) [姚振汉, 王海涛 2009 边界元法(北京: 高等教育出版社)第226页]
[12] Wang H T, Yao Z H, Wang P B 2005 Eng. Anal. Bound. Elem. 29 673
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