Abstract
As an inverse problem, particle reconstruction in tomographic particle image velocimetry attempts to solve a large-scale underdetermined linear system using an optimization technique. The most popular approach, the multiplicative algebraic reconstruction technique (MART), uses entropy as an objective function in the optimization. All available MART-based methods are focused on improving the efficiency and accuracy of particle reconstruction. However, those methods do not perform very well on dealing with ghost particles in highly seeded measurements. In this report, a new technique called dual-basis pursuit (DBP), which is based on the basis pursuit technique, is proposed for tomographic particle reconstruction. A template basis is introduced as a priori knowledge of a particle intensity distribution combined with a correcting basis to enable a full span of the solution space of the underdetermined linear system. A numerical assessment test with 2D synthetic images indicated that the DBP technique is superior to MART method, can completely recover a particle field when the number of particles per pixel (ppp) is less than 0.15, and can maintain a quality factor Q of above 0.8 for ppp up to 0.30. Unfortunately, the DBP method is difficult to utilize in 3D applications due to the cost of its excessive memory usage. Therefore, a dual-basis MART was designed that performed better than the traditional MART and can potentially be utilized for 3D applications.
Similar content being viewed by others
References
Elsinga G E, Scarano F, Wieneke B, et al. Tomographic particle image velocimetry. Exp Fluids, 2006, 41: 933–947
Scarano F. Tomographic PIV: Principles and practice. Meas Sci Tech, 2013, 24: 012001
Herman G T, Lent A. Iterative reconstruction algorithms. Comput Biol Med, 1976, 6: 273–294
Natterer F. Numerical methods in tomography. Acta Numer, 1999, 8: 107–141
Gordon R, Bender R, Herman G T. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. J Theor Biol, 1970, 29: 471–481
Atkinson C, Soria J. An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp Fluids, 2009, 47: 553–568
Gao Q, Wang H P, Shen G X. Review on development of volumetric particle image velocimetry. Chin Sci Bull, 2013, 58: 4541–4556
Elsinga G, Westerweel J, Scarano F, et al. On the velocity of ghost particles and the bias errors in Tomographic-PIV. Exp Fluids, 2011, 50: 825–838
Michaelis D, Novara M, Scarano F, et al. Comparison of volume reconstruction techniques at different particle densities. In: 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2010
Petra S, Schnörr C, Schröder A, et al. Tomographic image reconstruction in experimental fluid dynamics: Synopsis and problems. In: Ion S, Marinoschi G, Popa C, eds. Mathematical Modelling of Environmental and Life Sciences Problems, Bucuresti: Ed. Acad Romane, 2007. 1–21
Westerweel J, Elsinga G E, Adrian R J. Particle image velocimetry for complex and turbulent flows. Annu Rev Fluid Mech, 2013, 45: 409–436
Worth N A, Nickels T B. Acceleration of Tomo-PIV by estimating the initial volume intensity distribution. Exp Fluids, 2008, 45: 847–856
Donoho D L. Compressed sensing. IEEE T Inform Theory, 2006, 52: 1289–1306
Petra S, Schnörr C. TomoPIV meets compressed sensing. In: ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics, Athens, Greece, 2010
Petra S, Schröder A, Schnörr C. 3D tomography from few projections in experimental fluid dynamics. Imag Meas Meth Flow Anal, 2009. 63–72
Lamarche F, Leroy C. Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals. Comput Phys Commun, 1990, 59: 359–369
Schanz D, Gesemann S, Schröder A, et al. Non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. Meas Sci Tech, 2013, 24: 024009
Champagnat F, Cornic P, Cheminet A, et al. Tomographic PIV: particles vs blobs. In: 10th International Symposium on Particle Image Velocimetry, Delft, The Netherlands, 2013
Discetti S, Natale A, Astarita T. Spatial filtering improved tomographic PIV. Exp Fluids, 2013, 54: 1–13
Sebastian G, Daniel S, Andreas S, et al. Recasting Tomo-PIV reconstruction as constrained and L1-regularized non-linear least squares problem. In: 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2010
Barbu I, Herzet C, Memin E. Sparse models and pursuit algorithms for piv tomography. In: Forum on Recent Developments in Volume Reconstruction Techniques Applied to 3D Fluid and Solid Mechanics, Futuroscope Chasseneuil, France, 2011
Mallat S G, Zhang Z. Matching pursuits with time-frequency dictionaries. IEEE T Signal Proces, 1993, 41: 3397–3415
Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM J Sci Comput, 1998, 20: 33–61
Cornic P, Champagnat F, Cheminet A, et al. Computationally efficient sparse algorithms for tomographic PIV Reconstruction. In: 10th International Symposium on Particle Image Velocimetry, Delft, The Netherlands, 2013
Adrian R J, Westerweel J. Particle Image Velocimetry. 2nd ed. London: Cambridge University Press, 2010
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ye, Z., Gao, Q., Wang, H. et al. Dual-basis reconstruction techniques for tomographic PIV. Sci. China Technol. Sci. 58, 1963–1970 (2015). https://doi.org/10.1007/s11431-015-5909-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-015-5909-x