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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1017–1026

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

Samir Kumar Biswas, Rajan Kanhirodan, Ram Mohan Vasu, and Debasish Roy  »View Author Affiliations

JOSA A, Vol. 29, Issue 6, pp. 1017-1026 (2012)

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We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss–Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.

© 2012 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.0110) Imaging systems : Imaging systems
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: January 6, 2012
Revised Manuscript: March 7, 2012
Manuscript Accepted: March 8, 2012
Published: May 25, 2012

Virtual Issues
Vol. 7, Iss. 8 Virtual Journal for Biomedical Optics

Samir Kumar Biswas, Rajan Kanhirodan, Ram Mohan Vasu, and Debasish Roy, "Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography," J. Opt. Soc. Am. A 29, 1017-1026 (2012)

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  1. A. P. Gibson, J. Hebden, and Arridge, “Recent advances in diffuse optical tomography,” Phys. Med. Biol. 50, R1–R43 (2005). [CrossRef]
  2. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, 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).
  3. Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002). [CrossRef]
  4. 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]
  5. A. H. Heilscher, A. D. Close, and K. M. Hansen, “Gradient based iterative image reconstruction scheme for time resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999). [CrossRef]
  6. S. Arridge and J. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997). [CrossRef]
  7. 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]
  8. E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001). [CrossRef]
  9. B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001). [CrossRef]
  10. H. B. Jiang, Y. Xu, and N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media from continuous-wave data,” Opt. Express 7, 204–209 (2000). [CrossRef]
  11. Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002). [CrossRef]
  12. M. Schweiger and S. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998). [CrossRef]
  13. M. E. Kilmer, E. L. Miller, A. Barbaro, and D. A. Boas, “3D shape-based imaging for diffuse optical tomography,” Appl. Opt. 42, 3129–3144 (2003). [CrossRef]
  14. M. J. Holboke, B. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247 (2000). [CrossRef]
  15. H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001). [CrossRef]
  16. S. K. Biswas, R. Kanhirodan, R. M. Vasu, and D. Roy, “A pseudo-dynamical systems approach based on a quadratic approximation of update equations for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 1784–1795 (2011). [CrossRef]
  17. T. Raveendran, S. Gupta, R. M. Vasu, and D. Roy, “Pseudo-time particle filtering for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 2070–2081 (2011). [CrossRef]
  18. 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 (2009). [CrossRef]
  19. B. Kanmani and R. M. Vasu, “Diffuse optical tomography through solving a system of quadratic equations: theory and simulations,” Phys. Med. Biol. 51, 981–998 (2006). [CrossRef]
  20. C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comp. 19, 577–593 (1965). [CrossRef]
  21. S. Schlenkrich and A. Walther, “Global convergence of quasi-Newton methods based on adjoint Broyden updates,” Appl. Num. Math. 59, 1120–1136 (2009). [CrossRef]
  22. S. K. Biswas, K. Rajan, and R. M. Vasu, “Accelerated gradient based diffuse optical tomographic image reconstruction,” Med. Phys. 38, 539–547 (2011). [CrossRef]
  23. D. Roy, “Explorations of the phase space linearization method for deterministic and stochastic non-linear dynamical systems,” Nonlin. Dynam. 23, 225–258 (2000). [CrossRef]
  24. D. Roy, “A new numeric-analytical principle for nonlinear deterministic and stochastic dynamical systems,” Proc. R. Soc. Lond. A 457, 539–566 (2001). [CrossRef]
  25. S. Fantini, M. A. Franceschini, B. F. Joshua, B. Barbieri, and E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light emitting diode based technique,” Appl. Opt. 33, 5204–5213 (1994). [CrossRef]

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