OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 6477–6491

A trust region method in adaptive finite element framework for bioluminescence tomography

Bo Zhang, Xin Yang, Chenghu Qin, Dan Liu, Shouping Zhu, Jinchao Feng, Li Sun, Kai Liu, Dong Han, Xibo Ma, Xing Zhang, Jianghong Zhong, Xiuli Li, Xiang Yang, and Jie Tian  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6477-6491 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (340 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.

© 2010 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Image Processing

Original Manuscript: January 7, 2010
Revised Manuscript: February 11, 2010
Manuscript Accepted: March 11, 2010
Published: March 15, 2010

Virtual Issues
Vol. 5, Iss. 7 Virtual Journal for Biomedical Optics

Bo Zhang, Xin Yang, Chenghu Qin, Dan Liu, Shouping Zhu, Jinchao Feng, Li Sun, Kai Liu, Dong Han, Xibo Ma, Xing Zhang, Jianghong Zhong, Xiuli Li, Xiang Yang, and Jie Tian, "A trust region method in adaptive finite element framework for bioluminescence tomography," Opt. Express 18, 6477-6491 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. Weissleder and V. Ntziachristos, "Shedding light onto live molecular targets," Nature Medicine 9, 123−128 (2003). [CrossRef] [PubMed]
  2. V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nature Biotechnol. 23, 313−320 (2005). [CrossRef]
  3. M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, and J. H. Rao, "Self-illuminating quantum dot conjugates for in vivo imaging," Nature Biotechnol. 24, 339−343 (2006). [CrossRef]
  4. R. Weissleder and M. J. Pittet, "Imaging in the era of molecular oncology," Nature 452, 580−589 (2008). [CrossRef] [PubMed]
  5. J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7, 591−607 (2008). [CrossRef] [PubMed]
  6. V. Isakov, Inverse Problems for Partial Differential Equations (Springer-Verlag, New York, 1998).
  7. Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211−8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211. [CrossRef] [PubMed]
  8. C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, "Adaptive improved element free Galerkin method for quasi or multi spectral bioluminescence tomography," Opt. Express 17, 21925−21934 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21925. [CrossRef] [PubMed]
  9. J. Feng, K. Jia, C. Qin, G. Yan, S. Zhu, X. Zhang, J. Liu, and J. Tian, "Three-dimensional Bioluminescence Tomography based on Bayesian Approach," Opt. Express 17, 16834−16848 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16834. [CrossRef] [PubMed]
  10. Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, "Source Reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information," Opt. Express 17, 8062−8080 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8062. [CrossRef] [PubMed]
  11. Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, "Spectrallyresolved bioluminescence tomography with the third-order simplified spherical harmonics approximation," Phys. Medicine Bio. 59, 6477−6493 (2009).
  12. J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, "An optimal permissible source region strategy for multispectral bioluminescence tomography," Opt. Express 16, 15640−15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640. [CrossRef] [PubMed]
  13. Y. Lv, J. Tian, H. Li, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52, 1−16 (2007). [CrossRef]
  14. W. M. Han,W. X. Cong, and G. Wang, "Mathematical theory and numerical analysis of bioluminescence tomography," Inverse Problems 22, 1659−1675 (2006). [CrossRef]
  15. V. Soloviev, "Tomographic bioluminescence imaging with varying boundary conditions," Applied Optics 46, 2778−2784 (2007). [CrossRef] [PubMed]
  16. H. Dehghani, S. C. Davis, and B. W. Pogue, "Spectrally resolved bioluminescence tomography using the reciprocity approach," Medical Phys. 35, 4863−4871 (2008). [CrossRef] [PubMed]
  17. W. Gong, R. Li, N. N. Yan, and W. B. Zhao, "An improved error analysis for finite element approximation of bioluminescence tomography," J. Comp. Math. 26, 297−309 (2008).
  18. M. B. Unlu, and G. Gulsen, "Effects of the time dependence of a bioluminescent source on the tomographic reconstruction," Appl. Opt. 47, 799−806 (2008). [CrossRef]
  19. X. L. Cheng, R. F. Gong, and W. M. Han, "Numerical approximation of bioluminescence tomography based on a new formulation," J. Engin. Math. 63, 121−133 (2009). [CrossRef]
  20. M. Chua, and H. Dehghani, "Image reconstruction in diffuse optical tomography based on simplified spherical harmonics approximation," Opt. Express 17, 24208−24223, (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-26-24208. [CrossRef]
  21. K. Levenberg, "A method for the solution of certain nonlinear problems," Quart. Appl. Math. 2, 164−1681944).
  22. D. W. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," SIAM J. Appl. Math. 11, 431−441 (1963). [CrossRef]
  23. M. J. D. Powell, "A new algorithm for unconstrained optimization," in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds. (Academic Press, New York, 1970), 31−65.
  24. M. J. D. Powell, "Convergence properties of a class of minimization algorithms," in Nonlinear Programming, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds. (Academic Press, New York, 1975), 1−27.
  25. Y. Wang and Y. Yuan, "Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems," Inverse Problems 21, 821−838, (2005). [CrossRef]
  26. C. Contag and M. H. Bachmann, "Advances in Bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235−260 (2002). [CrossRef] [PubMed]
  27. V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence molecular tomography resolves protease activity in vivo," Nat. Med. 8, 757−760 (2002). [CrossRef] [PubMed]
  28. R. Schultz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imag. 23, 492−500 (2004). [CrossRef]
  29. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, "A finite element approach for modeling photon transport in tissue," Med. Phys. 20, 299−309 (1993). [CrossRef] [PubMed]
  30. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779−1792 (1995). [CrossRef] [PubMed]
  31. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis (Wiley, New York, 1976).
  32. S. S. Rao, The finite element method in engineering (Butterworth-Heinemann, Boston, 1999).
  33. W. Cong, D. Kumar, Y. Liu, A. Cong, and G. Wang, "A practical method to determine the light source distribution in bioluminescent imaging," Proc. SPIE 5535, 679−686 (2004). [CrossRef]
  34. W. Sun and Y. Yuan, "Chapter 6 Trust-Region Methods and Conic Model Methods" in Optimization Theory and Methods: Nonlinear Programming (Springer US, 2006).
  35. B. Zhang, J. Tian, D. Liu, L. Sun, X. Yang, and D. Han, "A multithread based new sparse matrix method in bioluminescence tomography", presented at Conference 7626 of SPIE on Medical Imaging, San Diego, USA, 13−18 February 2010.
  36. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50, 4225−4241 (2005). [CrossRef] [PubMed]
  37. L. H. Wang, S. L. Jacques, and L. Q. Zheng, "MCML-Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Meth. Prog. Biomed. 47, 131−146 (1995). [CrossRef]
  38. D. Boas, J. Culver, J. Stott, and A. Dunn, "Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head," Opt. Express 10, 159−169 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=OPEX-10-3-159. [PubMed]
  39. H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11, 1029−1038 (2004). [CrossRef] [PubMed]
  40. D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007). [CrossRef]
  41. J. Tian, J. Bai, X.-P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Bio. Mag. 27, 48−57 (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited