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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26589–26604

Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography

Okkyun Lee and Jong Chul Ye  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26589-26604 (2013)
http://dx.doi.org/10.1364/OE.21.026589


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Abstract

Some optical properties of a highly scattering medium, such as tissue, can be reconstructed non-invasively by diffuse optical tomography (DOT). Since the inverse problem of DOT is severely ill-posed and nonlinear, iterative methods that update Green’s function have been widely used to recover accurate optical parameters. However, recent research has shown that the joint sparse recovery principle can provide an important clue in achieving reconstructions without an iterative update of Green’s function. One of the main limitations of the previous work is that it can only be applied to absorption parameter reconstruction. In this paper, we extended this theory to estimate the absorption and scattering parameters simultaneously when the background optical properties are known. The main idea for such an extension is that a joint sparse recovery step gives us unknown fluence on the estimated support set, which eliminates the nonlinearity in an integral equation for the simultaneous estimation of the optical parameters. Our numerical results show that the proposed algorithm reduces the cross-talk artifacts between the parameters and provides improved reconstruction results compared to existing methods.

© 2013 OSA

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: September 3, 2013
Revised Manuscript: October 9, 2013
Manuscript Accepted: October 17, 2013
Published: October 28, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Okkyun Lee and Jong Chul Ye, "Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography," Opt. Express 21, 26589-26604 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26589


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References

  1. A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20, 435–442 (1997). [CrossRef] [PubMed]
  2. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag.18, 57–75 (2001). [CrossRef]
  3. D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab.20, 469–477 (2000). [CrossRef] [PubMed]
  4. V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: Applications to breast cancer,” Breast Cancer Res.3, 41–46 (2001). [CrossRef] [PubMed]
  5. R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med.9, 123–128 (2003). [CrossRef] [PubMed]
  6. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999). [CrossRef]
  7. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50, R1–R43 (2005). [CrossRef] [PubMed]
  8. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett.26, 893–895 (2001). [CrossRef]
  9. V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas,” J. Opt. Soc. Am. A18, 1336–1347 (2001). [CrossRef]
  10. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency-domain data: Simulation and experiment,” J. Opt. Soc. Am. A13, 253–266 (1996). [CrossRef]
  11. Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Frequency domain optical imaging of absorption and scattering distributions by a Born iterative method,” J. Opt. Soc. Am. A14, 325–342 (1997). [CrossRef]
  12. J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, “Optical diffusion tomography using iterative coordinate descent optimization in a Bayesian framework,” J. Opt. Soc. Am. A16, 2400–2412 (1999). [CrossRef]
  13. J. C. Ye, S. Y. Lee, and Y. Bresler, “Exact reconstruction formula for diffuse optical tomography using simultaneous sparse representation,” in International Symposium on Biomedical Imaging: From Nano to Macro, Paris, France (Institute of Electrical and Electronics Engineers, 2008), pp. 1621–1624.
  14. O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: Non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging30, 1129–1142 (2011). [CrossRef] [PubMed]
  15. J. Chen and X. Huo, “Theoretical results on sparse representations of multiple measurement vectors,” IEEE Trans. Signal Process.54, 4634–4643 (2006). [CrossRef]
  16. J. M. Kim, O. K. Lee, and J. C. Ye, “Compressive MUSIC: Revisiting the link between compressive sensing and array signal processing,” IEEE Trans. Inf. Theory58, 278–301 (2012). [CrossRef]
  17. A. Profio and G. Navarro, “Scientific basis of breast diaphanography,” Med. Phys.16, 60–65 (1989). [CrossRef] [PubMed]
  18. S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, and K. T. Moesta, “Assessment of the size, position, and optical properties of breast tumors in vivo by noninvasive optical methods,” Appl. Opt.37, 1982–1989 (1998). [CrossRef]
  19. A. E. Cerussi, D. Jakubowski, N. Shah, F. Bevilacqua, R. Lanning, A. J. Berger, D. Hsiang, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Spectroscopy enhances the information content of optical mammography,” J. Biomed. Opt.7, 60–71 (2002). [CrossRef] [PubMed]
  20. N. F. Boyd, J. W. Byng, R. A. Jong, E. K. Fishell, L. E. Little, A. B. Miller, G. A. Lockwood, D. L. Tritchler, and M. J. Yaffe, “Quantitative classification of mammographic densities and breast cancer risk: Results from the Canadian national breast screening study,” J. Natl. Cancer Inst.87, 670–675 (1995). [CrossRef] [PubMed]
  21. J. W. Byng, M. J. Yaffe, R. A. Jong, R. S. Shumak, G. A. Lockwood, D. L. Tritchler, and N. F. Boyd, “Analysis of mammographic density and breast cancer risk from digitized mammograms,” Radiographics18, 1587–1598 (1998). [PubMed]
  22. B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: Analysis of intersubject variability and menstrual cycle changes,” J. Biomed. Opt9, 541–552 (2004). [CrossRef] [PubMed]
  23. M. O’Leary, D. Boas, B. Chance, and A. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography,” Opt. Lett.20, 426–428 (1995). [CrossRef]
  24. J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, and S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett.24, 534–536 (1999). [CrossRef]
  25. T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett.26, 822–824 (2001). [CrossRef]
  26. J. Wang, S. D. Jiang, Z. Z. Li, R. M. diFlorio Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys.37, 3715–3724 (2010). [CrossRef] [PubMed]
  27. B. J. Hoenders, “Existence of invisible nonscattering objects and nonradiating sources,” J. Opt. Soc. Am. A14, 262–266 (1997). [CrossRef]
  28. S. Arridge and W. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett.23, 882–884 (1998). [CrossRef]
  29. V. Markel and J. Schotland, “Inverse problem in optical diffusion tomography. II. Role of boundary conditions,” J. Opt. Soc. Am. A19, 558–566 (2002). [CrossRef]
  30. L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (John Wiley, 2007).
  31. J. C. Ye, K. J. Webb, R. P. Millane, and T. J. Downar, “Modified distorted Born iterative method algorithm with an approximate Fréchet derivative for optical diffusion tomography,” J. Opt. Soc. Am. A16, 1814–1826 (1999). [CrossRef]
  32. M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory58, 1135–1146 (2012). [CrossRef]
  33. S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process.53, 2477–2488 (2005). [CrossRef]
  34. D. Malioutov, M. Cetin, and A. Willsky, “A sparse signal reconstruction perspective for source localization with sensor arrays,” IEEE Trans. Signal Process.53, 3010–3022 (2005). [CrossRef]
  35. D. P. Wipf and B. D. Rao, “An empirical Bayesian strategy for solving the simultaneous sparse approximation problem,” IEEE Trans. Signal Process.55, 3704–3716 (2007). [CrossRef]
  36. J. M. Kim, O. K. Lee, and J. C. Ye, “Improving noise robustness in subspace-based joint sparse recovery,” IEEE Trans. Signal Process.60, 5799–5809 (2012). [CrossRef]
  37. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004). [CrossRef]
  38. M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Trans. Image Process.20, 681–695 (2011). [CrossRef]
  39. Y. Pei, H. L. Graber, and R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express9, 97–109 (2001). [CrossRef] [PubMed]
  40. Y. Xu, X. Gu, T. Khan, and H. Jiang, “Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of DC data,” Appl. Opt.41, 5427–5437 (2002). [CrossRef] [PubMed]
  41. Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express17, 20178–20190 (2009). [CrossRef] [PubMed]
  42. B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: A 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52, 577–587 (2007). [CrossRef] [PubMed]
  43. 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]
  44. S. A. Prahl, “Optical Properties Spectra,” Oregon Medical Laser Clinic, 2001, http://omlc.ogi.edu/spectra/index.html .
  45. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, “Comparing images using the Hausdorff distance,” IEEE Trans. Pattern Anal. Mach. Intell.15, 850–863 (1993). [CrossRef]

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