OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 19 — Jul. 1, 2012
  • pp: 4501–4512

Total variation regularization for bioluminescence tomography with the split Bregman method

Jinchao Feng, Chenghu Qin, Kebin Jia, Shouping Zhu, Kai Liu, Dong Han, Xin Yang, Quansheng Gao, and Jie Tian  »View Author Affiliations

Applied Optics, Vol. 51, Issue 19, pp. 4501-4512 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1277 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l 2 and l 1 regularizations. However, l 2 regularization can oversmooth reconstructed images and l 1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l 2 and l 1 regularizations.

© 2012 Optical Society of America

OCIS Codes
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: July 28, 2011
Revised Manuscript: May 10, 2012
Manuscript Accepted: May 17, 2012
Published: June 29, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Jinchao Feng, Chenghu Qin, Kebin Jia, Shouping Zhu, Kai Liu, Dong Han, Xin Yang, Quansheng Gao, and Jie Tian, "Total variation regularization for bioluminescence tomography with the split Bregman method," Appl. Opt. 51, 4501-4512 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  2. G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010). [CrossRef]
  3. X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
  4. C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002). [CrossRef]
  5. D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009). [CrossRef]
  6. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010). [CrossRef]
  7. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity,” Opt. Express 18, 2894–2912 (2010). [CrossRef]
  8. H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006). [CrossRef]
  9. J. Feng, K. Jia, G. Yan, S. Zhu, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16, 15640–15654 (2008). [CrossRef]
  10. Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007). [CrossRef]
  11. 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). [CrossRef]
  12. Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010). [CrossRef]
  13. A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010). [CrossRef]
  14. K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).
  15. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268 (1992). [CrossRef]
  16. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004). [CrossRef]
  17. T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998). [CrossRef]
  18. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35, 3447–3458 (1996). [CrossRef]
  19. L. Yao and H. Jiang, “Enhancing finite element based photoacoustic tomography using total-variation minimization,” Appl. Opt. 50, 5031–5041 (2011). [CrossRef]
  20. L. Yao and H. Jiang, “Photoacoustic image reconstruction from few-detector and limited-angle data,” Biomed. Opt. Express 2, 2649–2654 (2011). [CrossRef]
  21. S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008). [CrossRef]
  22. A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005). [CrossRef]
  23. H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008). [CrossRef]
  24. J. Feng, K. Jia, C. Qin, G. Yan, X. Zhang, J. Liu, and J. Tian, “3D bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009). [CrossRef]
  25. G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004). [CrossRef]
  26. S. Osher, M. Burger, D. Glodfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation based image restoration,” Multiscale Model. Simul. 4, 460–489 (2005). [CrossRef]
  27. T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
  28. T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010). [CrossRef]
  29. J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009). [CrossRef]
  30. J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009). [CrossRef]
  31. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sci. 1, 143–168 (2008).
  32. J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011). [CrossRef]
  33. T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996). [CrossRef]
  34. M. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007). [CrossRef]
  35. J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010). [CrossRef]
  36. 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 Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).
  37. 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]

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