OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 10 — Jul. 19, 2010

Virtual sensors for 2D vector field tomography

Archontis Giannakidis, Leonidas Kotoulas, and Maria Petrou  »View Author Affiliations


JOSA A, Vol. 27, Issue 6, pp. 1331-1341 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001331


View Full Text Article

Enhanced HTML    Acrobat PDF (401 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We consider the application of tomography to the reconstruction of 2-D vector fields. The most convenient sensor configuration in such problems is the regular positioning along the domain boundary. However, the most accurate reconstructions are obtained by sampling uniformly the Radon parameter domain rather than the border of the reconstruction domain. This dictates a prohibitively large number of sensors and impractical sensor positioning. In this paper, we propose uniform placement of the sensors along the boundary of the reconstruction domain and interpolation of the measurements for the positions that correspond to uniform sampling in the Radon domain. We demonstrate that when the cubic spline interpolation method is used, a 60 times reduction in the number of sensors may be achieved with only about 10% increase in the error with which the vector field is estimated. The reconstruction error by using the same sensors and ignoring the necessity of uniform sampling in the Radon domain is in fact higher by about 30%. The effects of noise are also examined.

© 2010 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.0110) Imaging systems : Imaging systems
(110.6960) Imaging systems : Tomography
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

History
Original Manuscript: May 26, 2009
Revised Manuscript: January 28, 2010
Manuscript Accepted: February 10, 2010
Published: May 14, 2010

Virtual Issues
Vol. 5, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Archontis Giannakidis, Leonidas Kotoulas, and Maria Petrou, "Virtual sensors for 2D vector field tomography," J. Opt. Soc. Am. A 27, 1331-1341 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-27-6-1331


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. P. Juhlin, “Doppler tomography,” Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, October 28–31, 1993, San Diego, California, USA (1993) pp. 212–213. [CrossRef]
  2. Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16,12350–12361(2008). [CrossRef] [PubMed]
  3. B. M. Howe, P. F. Worcester, and R. C. Spindel, “Ocean acoustic tomography: Mesoscale velocity,” J. Geophys. Res. 92, 3785–3806 (1987). [CrossRef]
  4. W. Munk and C. Wunsch, “Observing the ocean in the 1990s,” Philos. Trans. R. Soc. London, Ser. A 307, 439–464 (1982). [CrossRef]
  5. D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991). [CrossRef]
  6. S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.
  7. D. M. Kramer and P. C. Lauterbur, “On the problem of reconstructing images of non-scalar parameters from projections. Applications to vector fields,” ISA Trans. 26, 2674–2677(1979). [CrossRef]
  8. S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imaging 4, 201–233(1982). [CrossRef] [PubMed]
  9. S. J. Norton, “Tomographic reconstruction of 2-D vector fields: Application to flow imaging,” Geophys. J. Int. 97, 161–168 (1988). [CrossRef]
  10. S. J. Norton, “Unique tomographic reconstruction of vector fields using boundary data,” IEEE Trans. Image Process. 1, 406–412 (1992). [CrossRef] [PubMed]
  11. H. Braun and A. Hauck, “Tomographic reconstruction of vector fields,” IEEE Trans. Signal Process. 39, 464–471(1991). [CrossRef]
  12. K. B. Winters and D. Rouseff, “A filtered backprojection method for the tomographic reconstruction of fluid vorticity,” Inverse Probl. 6, L33–L38(1990). [CrossRef]
  13. K. B. Winters and D. Rouseff, “Tomographic reconstruction of stratified fluid flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40, 26–33(1993). [CrossRef] [PubMed]
  14. M. Zahn, “Transform relationship between Kerr-effect optical phase shift and non-uniform electric field distributions,” IEEE Trans. Dielectr. Electr. Insul. 1, 235–246(1994). [CrossRef]
  15. H. M. Hertz, “Kerr effect tomography for nonintrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Opt. 25, 914–921(1986). [CrossRef] [PubMed]
  16. H. K. Aben, “Kerr effect tomography for general axisymmetric field,” Appl. Opt. 26, 2921–2924(1987). [CrossRef] [PubMed]
  17. N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995). [CrossRef]
  18. G. W. Faris and R. L. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212(1988). [CrossRef] [PubMed]
  19. V. A. Sharafutdinov, “Tomographic problem of photoelasticity,” Proc. SPIE 1843, 234–243(1992). [CrossRef]
  20. H. Aben and A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221(1997). [CrossRef]
  21. A. Schwarz, “Three-dimensional reconstruction of temperature and velocity fields in a furnace,” Proceedings of ECAPT, The European Concerted Action on Process Tomography (International Society for Industrial Process Tomography, 1994), pp. 227–233.
  22. S. E. Segre, “The measurement of poloidal magnetic field in a tokamak by the change of polarization of an electromagnetic wave,” Plasma Phys. 20, 295–307(1978). [CrossRef]
  23. P. Juhlin, “Principles of Doppler Tomography,” Lund Institute of Technology, Sweden, Department of Mathematics, LUTFD2/(TFMA-92)/7002+17P, August (1992).
  24. M. Petrou and A. Giannakidis, “Complete tomographic reconstruction of 2-d vector fields using a system of linear equations,” Proceedings of the 12th Annual Medical Image Understanding and Analysis Conference (MIUA 2008) July 2-3, 2008, Dundee, Scotland, UK, pp. 132–136.
  25. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).
  26. M. Petrou and A. Kadyrov, “Affine invariant features from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 30–44(2004). [CrossRef] [PubMed]
  27. A. Kadyrov and M. Petrou, “Affine parameter estimation from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1631–1645(2006). [CrossRef] [PubMed]
  28. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing(American Mathematical Society, 2002).
  29. H. R. Schwarz, Numerische Mathematik (B. G. Teubner, 1986).
  30. H. Schwetlick and H. Kretzschmar, Numerische Verfahren fur Naturwissenschaftler und Ingenieure (Fachbuchverlag, 1991).
  31. I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).
  32. C. de Boor, A Practical Guide to Splines (Springer-Verlag, 1978). [CrossRef]
  33. C. Habermann and F. Kindermann, “Multidimensional spline interpolation: Theory and applications,” Comput. Econ. 30, 153–169(2007). [CrossRef]
  34. R. M. Rangayyan, M. Ciuc, and F. Faghih, “Adapted-neighborhood filtering of images corrupted by signal-dependent noise,” Appl. Opt. 37, 4477–4487(1998). [CrossRef]
  35. T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005). [PubMed]
  36. G. Krüger and G. H. Glover, “Physiological noise in oxygenation-sensitive magnetic resonance imaging,” Magn. Reson. Med. 46, 631–677(2001). [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  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited