OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 1 — Feb. 4, 2013

Total variation regularization for 3D reconstruction in fluorescence tomography: experimental phantom studies

Ali Behrooz, Hao-Min Zhou, Ali A. Eftekhar, and Ali Adibi  »View Author Affiliations


Applied Optics, Vol. 51, Issue 34, pp. 8216-8227 (2012)
http://dx.doi.org/10.1364/AO.51.008216


View Full Text Article

Enhanced HTML    Acrobat PDF (806 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Fluorescence tomography (FT) is depth-resolved three-dimensional (3D) localization and quantification of fluorescence distribution in biological tissue and entails a highly ill-conditioned problem as depth information must be extracted from boundary measurements. Conventionally, L2 regularization schemes that penalize the Euclidean norm of the solution and possess smoothing effects are used for FT reconstruction. Oversmooth, continuous reconstructions lack high-frequency edge-type features of the original distribution and yield poor resolution. We propose an alternative regularization method for FT that penalizes the total variation (TV) norm of the solution to preserve sharp transitions in the reconstructed fluorescence map while overcoming ill-posedness. We have developed two iterative methods for fast 3D reconstruction in FT based on TV regularization inspired by Rudin–Osher–Fatemi and split Bregman algorithms. The performance of the proposed method is studied in a phantom-based experiment using a noncontact constant-wave trans-illumination FT system. It is observed that the proposed method performs better in resolving fluorescence inclusions at different depths.

© 2012 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.6950) Image processing : Tomographic image processing
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.5280) Medical optics and biotechnology : Photon migration

ToC Category:
Image Processing

History
Original Manuscript: May 25, 2012
Revised Manuscript: August 17, 2012
Manuscript Accepted: October 16, 2012
Published: November 30, 2012

Virtual Issues
Vol. 8, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Ali Behrooz, Hao-Min Zhou, Ali A. Eftekhar, and Ali Adibi, "Total variation regularization for 3D reconstruction in fluorescence tomography: experimental phantom studies," Appl. Opt. 51, 8216-8227 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-51-34-8216


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006). [CrossRef]
  2. V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, and R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imaging 1, 82–88 (2002). [CrossRef]
  3. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, 1997).
  4. S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066–4082 (2007). [CrossRef]
  5. A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, and S. R. Arridge, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696–6716 (2007). [CrossRef]
  6. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. SevickMuraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99, 9619–9624 (2002). [CrossRef]
  7. Y. Lin, H. Yan, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography with functional and structural a priori information,” Appl. Opt. 48, 1328–1336 (2009). [CrossRef]
  8. A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13, 9847–9857 (2005). [CrossRef]
  9. X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15, 18300–18317 (2007). [CrossRef]
  10. J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general Lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imag. 29, 1075–1087 (2010). [CrossRef]
  11. P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46, 1679–1685 (2007). [CrossRef]
  12. D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010). [CrossRef]
  13. D. Han, X. Yang, K. Liu, C. Qin, B. Zhang, X. Ma, and J. Tian, “Efficient reconstruction method for L1 regularization in fluorescence molecular tomography,” Appl. Opt. 49, 6930–6937 (2010). [CrossRef]
  14. J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imag. 30, 1143–1153 (2011). [CrossRef]
  15. R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970). [CrossRef]
  16. R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
  17. X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, and B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47, N1–N10 (2002). [CrossRef]
  18. M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt. 49, 3741–3747 (2010). [CrossRef]
  19. J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459–1476 (2012). [CrossRef]
  20. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  21. H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element based algorithm and simulations,” Appl. Opt. 37, 5337–5343 (1998). [CrossRef]
  22. C. L. Lawson and R J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).
  23. J. A. Fessler and W. L. Rogers, “Spatial resolution properties of penalized-likelihood image reconstruction: Spatial-invariant tomographs,” IEEE Trans. Image Process. 9, 1346–1358 (1996). [CrossRef]
  24. H. Gao and H. K. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation. Part 2: total variation and l1 data fidelity,” Opt. Express 18, 2894–2912 (2010). [CrossRef]
  25. P. Kisilev, M. Zibulevsky, and Y. Zeevi, “Wavelet representation and total variation regularization in emission tomography,” in 2001 International Conference on Image Processing (IEEE, 2001), Vol. 1, pp. 702–705. [CrossRef]
  26. D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19, S165–S187 (2003). [CrossRef]
  27. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D. 60, 259–268 (1992). [CrossRef]
  28. T. Goldstein and S. Osher, “The Split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009). [CrossRef]
  29. J. F. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” SIAM J. Multisc. Model. Simul.8, 337–369 (2009).
  30. R. Courant, K. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74 (1928). [CrossRef]
  31. P. C. Hansen, “The L-curve and its use in the numerical treatment of inverse problems,” in Computational Inverse Problems in Electrocardiology, P. D. Johnston, ed. (WIT Press, 2001), pp. 119–142.
  32. X. Liu and L. Huang, “Split Bregman iteration algorithm for total bounded variation regularization based image deblurring,” J. Math. Anal. Appl. 372, 486–495 (2010). [CrossRef]
  33. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995).
  34. A. Michelson, Studies in Optics (University of Chicago, 1927).
  35. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media using a normalized born approximation,” Opt. Lett. 26, 893–895 (2001). [CrossRef]
  36. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997). [CrossRef]
  37. R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994). [CrossRef]
  38. S. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proces. 9, 1532–1546 (2000). [CrossRef]
  39. 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]

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