Experiments in Fluids

, 47:553 | Cite as

An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

  • Callum AtkinsonEmail author
  • Julio Soria
Research Article


To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.


Weighting Matrix Turbulent Boundary Layer Reconstruction Quality Algebraic Reconstruction Technique Ghost Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The support of Australian Research Council for this work is gratefully acknowledged. C. Atkinson was supported by an Eiffel Fellowship and an Australian Postgraduate Scholarship while undertaking this research. The authors would also like to thank the reviewers for their helpful comments.


  1. Andersen AH, Kak AC (1984) Simultaneous algebraic reconstruction technique (sart): a superior implementation of the art algorithm. Ultras Imaging 6:81–94CrossRefGoogle Scholar
  2. Atkinson CH, Soria J (2007a) Algebraic reconstruction techniques for tomographic particle image velocimetry. In: Proceedings of 16th Australasian fluid mechanics conference, Gold CoastGoogle Scholar
  3. Atkinson CH, Soria J (2007b) Multi-camera digital holographic piv: tomographic dhpiv. In: Proceedings of 16th Australasian fluid mechanics conference, Gold CoastGoogle Scholar
  4. Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41:933–947CrossRefGoogle Scholar
  5. Elsinga GE, Adrian RJ, van Oudheusden BW, Scarano F (2007) Tomographic-piv investigation of a high reynolds number turbulent boundary layer. In: Proceedings of 7th international symposium on particle image velocimetry, RomaGoogle Scholar
  6. Frigo M, Johnson SG (2005) The design and implementation of fftw3. Proc IEEE 93(2):216–231CrossRefGoogle Scholar
  7. Gordon R, Bender R, Herman GT (1970) Algebraic reconstruction techniques (art) for three-dimensional electron microscopy and x-ray photography. J Theor Biol 29:471CrossRefGoogle Scholar
  8. Hain R, Kähler CJ, Michaelis D (2008) Tomographic and time resolved piv measurements on a finite cylinder mounted on a flat plate. Exp Fluids 45:715–724CrossRefGoogle Scholar
  9. Herman GT, Lent A (1976) Iterative reconstruction algorithms. Comput Biol Med 6:273–294CrossRefGoogle Scholar
  10. Herpin S, Wong C, Stanislas M, Soria J (2008) Stereoscopic piv measurements of a turbulent boundary layer with a large spatial dynamic range. Exp Fluids 45:745–763CrossRefGoogle Scholar
  11. Lamarche F, Leroy C (1990) Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals. Comput Phys Commun 59:359–369CrossRefMathSciNetGoogle Scholar
  12. Michael YC, Yang KT (1991) Recent developments in axial tomography for heat transfer and fluid flow studies. Exp Therm Fluid Sci 4:637–647CrossRefGoogle Scholar
  13. Mishra D, Muralidhar K, Munshi P (1999) A robust mart algorithm for tomographic applications. Numer Heat Transf Part B 35:485–506CrossRefGoogle Scholar
  14. Mueller K, Yagel R (1999) On the use of graphics hardware to accelerate algebraic reconstruction methods. In: SPIE conference on physics of medical imaging, San DiegoGoogle Scholar
  15. Natterer F (1986) The mathematics of computerized tomography. Wiley, ChichesterzbMATHGoogle Scholar
  16. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1988) Numerical recipes in C : the art of scientific computing, 2nd edn. Cambridge University Press, CambridgezbMATHGoogle Scholar
  17. Scarano F, Elsinga GE, Bocci E, van Oudheusden BW (2006) Investigation of 3-d coherent structures in the turbulent cylinder wake using tomo-piv. In: 13th international symposium on applications of laser techniques to fluid mechanics, LisbonGoogle Scholar
  18. Schröder A, Geisler R, Michaelis D (2007) Flow structures in a tripped turbulent boundary layer flow—an investigation using time-resolved tomographic piv. In: Proceedings of 7th international symposium on particle image velocimetry, RomaGoogle Scholar
  19. Schröder A, Geisler R, Staack K, Wieneke B, Elsinga GE, Scarano F, Henning A (2008) Lagrangian and eulerian views into a turbulent boundary layer flow using time-resolved tomographic piv. In: 14th international symposium on applications of laser techniques to fluid mechanics, LisbonGoogle Scholar
  20. Soloff SM, Adrian RJ, Liu ZC (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8:144–1454CrossRefGoogle Scholar
  21. Soria J (1996) An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp Therm Fluid Sci 12:221–233CrossRefGoogle Scholar
  22. Soria J, Atkinson C (2007) Multi-camera digital holographic imaging piv versus tomographic imaging piv—comparison and contrast of these two 3c-3d piv techniques. In: Proceedings of international workshop on digital holographic reconstruction and optical tomography for engineering applications, Loughborough UniversityGoogle Scholar
  23. Soria J, Atkinson C (2008) Towards 3c-3d digital holographic fluid velocity vector field measurement—tomographic digital holographic piv (tomo-hpiv). Meas Sci Technol 19:1–12CrossRefGoogle Scholar
  24. Westerweel J, Scarano F (2005) Universal outlier detection for piv data. Exp Fluids 39:1096–1100CrossRefGoogle Scholar
  25. Wieneke B (2008) Volume self-calibration for 3d particle image velocimetry. Exp Fluids 45(4):549–556CrossRefGoogle Scholar
  26. Wieneke B, Taylor S (2006) Fat-sheet piv with computation of gull 3d-strain tensor using tomographic reconstruction. In: 13th international symposium on applications of laser techniques to fluid mechanics, LisbonGoogle Scholar
  27. Worth NA, Nickels TB (2008) Acceleration of tomo-piv by estimating the initial volume intensity distribution. Exp Fluids 45(5):847–856CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace EngineeringMonash UniversityMelbourneAustralia

Personalised recommendations