OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 9 — Oct. 3, 2011

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

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

JOSA A, Vol. 28, Issue 8, pp. 1784-1795 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1739 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

© 2011 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: April 22, 2011
Revised Manuscript: June 12, 2011
Manuscript Accepted: June 15, 2011
Published: August 1, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Samir Kumar Biswas, Rajan Kanhirodan, Ram Mohan Vasu, and Debasish Roy, "Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography," J. Opt. Soc. Am. A 28, 1784-1795 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Muzi, A. P. Lyons, and E. Pouliquen, “Use of X-ray computed tomography for the estimation of parameters relevant to the modeling of acoustic scattering from the seafloor,” Nucl. Instrum. Methods Phys. Res. B 213, 491–497 (2004). [CrossRef]
  2. A. Ishimaru, “Diffusion of light in turbid material,” Appl. Opt. 28, 2210–2215 (1989). [CrossRef] [PubMed]
  3. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336(1989). [CrossRef] [PubMed]
  4. A. P. Gibson, J. Hebden, and Arridge, “Recent advantages in diffuse optical tomography,” Phys. Med. Biol. 50, R1–R43(2005). [CrossRef] [PubMed]
  5. S. R. Arridge and M. Schweiger, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999). [CrossRef]
  6. M. Cheny, D. Issacson, and J. C. Newell, “Electrical impedance tomography,” SIAM Rev. 41, 85–101 (1999). [CrossRef]
  7. A. Whitten and J. E. Molyneux, “Geophysical imaging with arbitrary source illumination,” IEEE Trans. Geosci. Remote Sens. 26, 409–419 (1988). [CrossRef]
  8. 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]
  9. A. D. Close and A. H. Heilscher, “Optical tomography using time independent equation of radiative transfer—Part 2: inverse model,” J. Quant. Spectrosc. Radiat. Transfer 72715–732(2002). [CrossRef]
  10. K. Levenberg, “A method for the solution of certain non-linear problems in least-squares,” Q. J. Appl. Math. 2, 164–168(1944).
  11. D. W. Marquardt, “An algorithm for the least-square estimation of non-linear parameters,” SIAM J. Appl. Math. 11, 431–441(1963). [CrossRef]
  12. U. Ascher, E. Haber, and H. Huang, “On effective methods for implicit piecewise smooth surface recovery,” SIAM J. Comput. 28, 339–358 (2006). [CrossRef]
  13. K. van den Doel and U. Ascher, “On level set regularization for highly ill-posed distributed parameter estimation problems,” J. Comput. Phys. 216, 707–723 (2006). [CrossRef]
  14. C. Vogel, Computational Methods for Inverse Problems (SIAM, 2002). [CrossRef]
  15. J. E. Dennis, Jr., and R. B. Schnabel, “Quasi Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, 1983).
  16. 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]
  17. S. K. Biswas, K. Rajan, and R. M. Vasu, “Interior photon absorption based adaptive regularization improves diffuse optical tomography,” Proc. SPIE 7546, 754611 (2010). [CrossRef]
  18. A. D. Klose and A. H. Heilscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19387–409 (2003). [CrossRef]
  19. T. J. Ypma, “Historical development of the Newton-Raphson method,” SIAM Rev. 37, 531–551 (1995). [CrossRef]
  20. F. Hettlich and W. Rundell, “A second degree method for nonlinear inverse problem,” SIAM J. Numer. Anal. 37, 587–620(2000). [CrossRef]
  21. 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] [PubMed]
  22. S. R. Arridge and M. Schweiger, “A gradient based optimization scheme for optical tomography,” Opt. Express 2, 213–226(1998). [CrossRef] [PubMed]
  23. B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. London Ser. A 465, 1561–1579 (2009). [CrossRef]
  24. 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]
  25. G. H. Gulub, P. C. Hansen, and D. O’Leary, “Tikhonov regularization and total least squares,” SIAM. J. Matrix Anal. Appl. 21, 185–194 (1999). [CrossRef]
  26. D. Roy, “A numeric-analytic technique non-linear deterministic and stochastic dynamical systems,” Proc. R. Soc. London Ser. A 457, 539–566 (2001). [CrossRef]
  27. D. Roy, “Phase space linearization for non-linear oscillator: deterministic and stochastic systems,” J. Sound Vib. 231, 307–341(2000). [CrossRef]
  28. S. K. Biswas, K. Rajan, and R. M. Vasu, “Accelerated gradient based diffuse optical tomographic image reconstruction,” Med. Phys. 38, 539–547(2011). [CrossRef] [PubMed]
  29. B. Kanmani and R. M. Vasu, “Noise-tolerance analysis for detection and reconstruction of absorbing inhomogeneities with diffuse optical tomography using single- and phase-correlated dual-source schemes,” Phys. Med. Biol. 52, 1409–1429 (2007). [CrossRef] [PubMed]
  30. K. D. Paulsen and H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995). [CrossRef] [PubMed]
  31. S. K. Biswas, K. Rajan, and R. M. Vasu, “Diffuse optical tomographic imager using a single light source,” J. Appl. Phys. 105, 024702 (2009). [CrossRef]
  32. M. Autiero, R. Liuzzi, P. Riccio, and G. Roberti, “Determination of the concentration scaling law of the scattering coefficient of water solutions of Intralipid at 832 nm by comparision between collimated detection and Monte Carlo simulations,” Lasers Surg. Med. 36, 414–422 (2005). [CrossRef] [PubMed]

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

OSA is a member of CrossRef.

CrossCheck Deposited