OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 10 — Oct. 1, 2009
  • pp: 2257–2268

Approximation errors and model reduction in three-dimensional diffuse optical tomography

Ville Kolehmainen, Martin Schweiger, Ilkka Nissilä, Tanja Tarvainen, Simon R. Arridge, and Jari P. Kaipio  »View Author Affiliations

JOSA A, Vol. 26, Issue 10, pp. 2257-2268 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (548 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Model reduction is often required in diffuse optical tomography (DOT), typically because of limited available computation time or computer memory. In practice, this means that one is bound to use coarse mesh and truncated computation domain in the model for the forward problem. We apply the (Bayesian) approximation error model for the compensation of modeling errors caused by domain truncation and a coarse computation mesh in DOT. The approach is tested with a three-dimensional example using experimental data. The results show that when the approximation error model is employed, it is possible to use mesh densities and computation domains that would be unacceptable with a conventional measurement error model.

© 2009 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Image Processing

Original Manuscript: June 5, 2009
Revised Manuscript: August 20, 2009
Manuscript Accepted: August 27, 2009
Published: September 25, 2009

Ville Kolehmainen, Martin Schweiger, Ilkka Nissilä, Tanja Tarvainen, Simon R. Arridge, and Jari P. Kaipio, "Approximation errors and model reduction in three-dimensional diffuse optical tomography," J. Opt. Soc. Am. A 26, 2257-2268 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41-93 (1999). [CrossRef]
  2. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1-43 (2005). [CrossRef]
  3. B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse imaging technologies for breast cancer management,” Med. Phys. 35, 2443-2451 (2008). [CrossRef] [PubMed]
  4. S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, “Approximation errors and model reduction with an application in optical diffusion tomography,” Inverse Probl. 22, 175-195 (2006). [CrossRef]
  5. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems (Applied Mathematical Sciences, Springer, 2005).
  6. J. Kaipio and E. Somersalo, “Statistical inverse problems: Discretization, model reduction and inverse crimes,” J. Comput. Appl. Math. 198, 493-504 (2007). [CrossRef]
  7. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: Boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995). [CrossRef] [PubMed]
  8. J. Heino and E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559-573 (2002). [CrossRef]
  9. I. Nissilä, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiäinen, S. R. Arridge, and T. Katila, “Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography,”Rev. Sci. Instrum. 76, 1-10 (2005) article number 044302. [CrossRef]
  10. M. Schweiger, S. R. Arridge, and I. Nissilä, “Gauss-Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365-2386 (2005). [CrossRef] [PubMed]
  11. M. Schweiger and S. R. Arridge, “Application of temporal filters to time-resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999). [CrossRef] [PubMed]
  12. D. Calvetti and E. Somersalo, Introduction to Bayesian Scientific Computing (Springer, 2007).
  13. M. Schweiger and S. R. Arridge, “Optical tomography with local basis functions,” J. Electron. Imaging 12, 583-593 (2003). [CrossRef]
  14. A. Lehikoinen, S. Finsterle, A. Voutilainen, L. M. Heikkinen, M. Vauhkonen, and J. P. Kaipio, “Approximation errors and truncation of computational domains with application to geophysical tomography,” Inv. Probl. Imaging 1, 371-389 (2007). [CrossRef]
  15. M. Schweiger, I. Nissilä, D. A. Boas, and S. R. Arridge, “Image reconstruction in optical tomography in the presence of coupling errors,” Appl. Opt. 46, 2743-2756 (2007). [CrossRef] [PubMed]
  16. T. Tarvainen, V. Kolehmainen, M. Vauhkonen, A. Vanne, A. P. Gibson, M. Schweiger, S. R. Arridge, and J. P. Kaipio, “Computational calibration method for optical tomography,” Appl. Opt. 44, 1879-1888 (2006). [CrossRef]
  17. R. P. Brent, Algorithms for Minimization without Derivatives (Dover, 2002).
  18. J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

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