OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 24 — Nov. 26, 2007
  • pp: 15908–15919

An efficient Jacobian reduction method for diffuse optical image reconstruction

Matthew E. Eames, Brian W. Pogue, Phaneendra K. Yalavarthy, and Hamid Dehghani  »View Author Affiliations


Optics Express, Vol. 15, Issue 24, pp. 15908-15919 (2007)
http://dx.doi.org/10.1364/OE.15.015908


View Full Text Article

Enhanced HTML    Acrobat PDF (857 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Model based image reconstruction in Diffuse Optical Tomography relies on both the numerical accuracy of the forward model as well as the computational speed and efficiency of the inverse model. Most model based image reconstruction algorithms rely on Newton type inversion methods, whereby the inverse of a large Jacobian is approximated. In this work we present an efficient Jacobian reduction method which takes into account the total sensitivity of the imaging domain to the measured boundary data. It is shown using numerical and phantom data that by removing regions within the inverse model whose contribution to the measured data is less than 1%, it has no significant effect upon the estimated inverse problem, but does provide up to a 14 fold improvement in computational time.

© 2007 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(170.3660) Medical optics and biotechnology : Light propagation in tissues

ToC Category:
Image Processing

History
Original Manuscript: September 10, 2007
Revised Manuscript: November 2, 2007
Manuscript Accepted: November 8, 2007
Published: November 15, 2007

Virtual Issues
Vol. 2, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Matthew E. Eames, Brian W. Pogue, Phaneendra K. Yalavarthy, and Hamid Dehghani, "An efficient Jacobian reduction method for diffuse optical image reconstruction," Opt. Express 15, 15908-15919 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15908


Sort:  Year  |  Journal  |  Reset  

References

  1. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999). [CrossRef]
  2. H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, "Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results," Appl. Opt. 42, 135-145 (2003). [CrossRef] [PubMed]
  3. A. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50, R1-R43 (2005). [CrossRef] [PubMed]
  4. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, "Spectrally constrained Chromophore and Scattering NIR Tomography provides quantitative and robust reconstruction," Appl. Opt. 44, 1858-1869 (2005). [CrossRef] [PubMed]
  5. S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction," Technol. Cancer Res. Treat. 5, 513-526 (2005).
  6. A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, A. G. Yodh, "Diffuse optical tomography with spectral constraints and wavelength optimization," Appl. Opt. 44, 2082-2093 (2005). [CrossRef] [PubMed]
  7. B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, "Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography," Proc. Natl. Acad. Sci. U. S.A. 104, 12169-12174 (2007). [CrossRef] [PubMed]
  8. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, K. D. Paulsen, "Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in Vivo by near-infrared breast tomography," Proc. Natl. Acad. Sci. U. S.A. 100, 12349-12354 (2003). [CrossRef] [PubMed]
  9. R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, "Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: A case study with comparison to MRI," Med. Phys. 32, 1128-1139 (2005). [CrossRef] [PubMed]
  10. P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, "Structural information within regularization matrices improves near infrared diffuse optical tomography," Opt. Express 15, 8043-8058 (2007). [CrossRef] [PubMed]
  11. A. D. Klose and A. H. Hielscher, "Quasi Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003). [CrossRef]
  12. 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]
  13. A. D. Klose, and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999). [CrossRef] [PubMed]
  14. A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006). [CrossRef]
  15. O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998). [CrossRef]
  16. S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
  17. S. R. Arridge and M. Schwieger, "Gradient-based optimisation scheme for optical tomography," Opt. Express. 2, 212-226 (1998). [CrossRef]
  18. A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative image reconstruction scheme for time- resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999). [CrossRef] [PubMed]
  19. H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, "Three dimensional optical tomography: resolution in small object imaging," Appl. Opt. 42, 3117-3128 (2003). [CrossRef] [PubMed]
  20. K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization," Appl. Opt. 35, 3447-3458 (1996). [CrossRef] [PubMed]
  21. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, "Adaptive finite element based tomography for fluorescence optical imaging in tissue," Opt. Express 12, 5402-5417 (2004). [CrossRef] [PubMed]
  22. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, "Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis," Opt. Express 14, 6113-6127 (2006). [CrossRef] [PubMed]
  23. M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging," Inverse Probl. 23, 1135-1160 (2007). [CrossRef]
  24. M. Molinari, B. H. Blott, S. J. Cox, G. J. Daniell, "Optimal imaging with adaptive mesh refinement in electrical impedance tomography," Physiol. Meas. 23, 121-128 (2002). [CrossRef] [PubMed]
  25. H. Dehghani and M , Soleimani, "Numerical modelling errors in electrical impedance tomography," Physiol Meas 28, S45-S55 (2007). [CrossRef]
  26. 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]
  27. S. Srinivasan, B. W. Pogue, H. Dehghani, F. Leblond, and X. Intes, "A data subset algorithm for computationally efficient reconstruction of 3-D spectral imaging in diffuse optical tomography," Opt. Express 14, 5394-5410 (2006). [CrossRef] [PubMed]
  28. D. W. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," Appl. Math 11, 431-441 (1963). [CrossRef]
  29. J. R. Westlake, A handbook of numerical matrix inversion and solution of linear equations (John Wiley & Sons Inc, New York, 1968).

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