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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 10 — Oct. 1, 2011
  • pp: 2070–2081

Pseudo-time particle filtering for diffuse optical tomography

Tara Raveendran, Saurabh Gupta, Ram Mohan Vasu, and Debasish Roy  »View Author Affiliations


JOSA A, Vol. 28, Issue 10, pp. 2070-2081 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002070


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Abstract

We recast the reconstruction problem of diffuse optical tomography (DOT) in a pseudo-dynamical framework and develop a method to recover the optical parameters using particle filters, i.e., stochastic filters based on Monte Carlo simulations. In particular, we have implemented two such filters, viz., the bootstrap (BS) filter and the Gaussian-sum (GS) filter and employed them to recover optical absorption coefficient distribution from both numerically simulated and experimentally generated photon fluence data. Using either indicator functions or compactly supported continuous kernels to represent the unknown property distribution within the inhomogeneous inclusions, we have drastically reduced the number of parameters to be recovered and thus brought the overall computation time to within reasonable limits. Even though the GS filter outperformed the BS filter in terms of accuracy of reconstruction, both gave fairly accurate recovery of the height, radius, and location of the inclusions. Since the present filtering algorithms do not use derivatives, we could demonstrate accurate contrast recovery even in the middle of the object where the usual deterministic algorithms perform poorly owing to the poor sensitivity of measurement of the parameters. Consistent with the fact that the DOT recovery, being ill posed, admits multiple solutions, both the filters gave solutions that were verified to be admissible by the closeness of the data computed through them to the data used in the filtering step (either numerically simulated or experimentally generated).

© 2011 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(170.6960) Medical optics and biotechnology : Tomography
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

History
Original Manuscript: June 2, 2011
Revised Manuscript: August 3, 2011
Manuscript Accepted: August 4, 2011
Published: September 13, 2011

Virtual Issues
Vol. 6, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Tara Raveendran, Saurabh Gupta, Ram Mohan Vasu, and Debasish Roy, "Pseudo-time particle filtering for diffuse optical tomography," J. Opt. Soc. Am. A 28, 2070-2081 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-10-2070


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References

  1. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003). [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(6), 57–75(2001). [CrossRef]
  3. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, O. K. S., U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001). [PubMed]
  4. B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivocharacterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000). [CrossRef] [PubMed]
  5. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999). [CrossRef]
  6. P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34, 2085–2098 (2007). [CrossRef] [PubMed]
  7. C. R. Vogel, Computational Methods for Inverse Problems(Academic, 2002). [CrossRef]
  8. P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Rev. 34, 561–580 (1992). [CrossRef]
  9. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of the Inverse Problem (Academic, 1996). [CrossRef]
  10. V. Kolehmainen, S. Prince, S. R. Arridge, and J. P. Kaipo, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003). [CrossRef]
  11. M. J. Eppstein, D. E. Dougherty, T. L. Troy, and E. M. Sevic-Muraca, “Biomedical optical tomography using dynamic parametrization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999). [CrossRef]
  12. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Baysian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99, 9619–9624 (2002). [CrossRef] [PubMed]
  13. M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imag. 20, 147–163 (2001). [CrossRef]
  14. B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009). [CrossRef]
  15. B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561–1579 (2009). [CrossRef]
  16. A. Doucet, S. Godsill, and C. Andrieu, “On sequential Monte Carlo sampling methods for Bayesian filtering,” Stat. Comput. 10, 197–208 (2000). [CrossRef]
  17. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice (Academic, 2001).
  18. S. Arulampalam, N. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188(2002). [CrossRef]
  19. N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” in IEE Proceedings F Radar and Signal Processing (IEEE, 1993), Vol.  140, pp. 107–113. [CrossRef]
  20. K. Murphy and S. Russell, “Rao-Blackwellised particle filtering for dynamic Bayesian networks,” in Sequential Monte Carlo Methods in Practice, A.Doucet, N.de Freitas, and N.Gordon, eds. (Academic2001), pp. 499–515.
  21. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle filtering,” IEEE Trans. Signal Process. 51, 2602–2612 (2003). [CrossRef]
  22. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle filtering for dynamic state space models,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2001), pp. 3465–3468.
  23. M. Schweiger, S. R. Arridge, and I. Nissila, “Gauss–Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005). [CrossRef] [PubMed]
  24. K. Levenberg, “A method for the solution of certain nonlinear problems in least squares,” Quart. Appl. Math. 2, 164–168(1944).
  25. D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441(1963). [CrossRef]
  26. D. Roy, “Explorations of the phase space linearization method for deterministic and stochastic non-linear dynamical systems,” Nonlinear Dyn. 23, 225–258 (2000). [CrossRef]
  27. D. Roy, “A new numeric-analytical principle for nonlinear deterministic and stochastic dynamical systems,” Proc. R. Soc. London Ser. A 457, 539–566 (2001). [CrossRef]
  28. G. Kallianpur, Stochastic Filtering Theory (Academic, 1980).
  29. A. D. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. Arridge, “3D shape based reconstruction of experimental data in diffuse optical tomography,” Opt. Express 17, 18940–18956(2009). [CrossRef]
  30. R. Lipster and A. Shiryaev, Statistics of Random Processes(Academic, 2001).
  31. P. Fernhead, “Sequential Monte Carlo methods in filter theory,” Ph.D. thesis (University of Oxford, 1998).
  32. S. Gupta, P. K. Yalavarthy, D. Roy, D. Piao, and R. M. Vasu, “Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography,” Med. Phys. 36, 5559–5567 (2009). [CrossRef]
  33. B. Banerjee, D. Roy, and R. M. Vasu, “Efficient implementations of a pseudo-dynamical stochastic filtering strategy for static elastography,” Med. Phys. 36, 3470–3476 (2009). [CrossRef] [PubMed]

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