Skip to main content
Log in

Digital in-line particle holography: twin-image suppression using sparse blind source separation

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We propose a robust autofocus method for reconstructing digital holograms and twin-image removal based on blind source separation approach. The method is made up of two components: an efficient quincunx lifting scheme based on wavelet packet transform, whose role is to maximize a sharpness metric related to the sparseness of the input holograms, and a geometric unmixing algorithm, which achieves the separation task. Experimental results confirm the ability of sparse blind source separation to discard the unwanted twin-image from in-line digital holograms of particles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Gabor, D.: A new microscopic principle. Nature 161, 777–778 (1948)

    Article  Google Scholar 

  2. Leith, E.N., Upatnieks, J.: Reconstructed wavefronts and communication theory. J. Opt. Soc. Am. 52, 1123–1130 (1962)

    Article  Google Scholar 

  3. Onural, L.: Diffraction from a wavelet point of view. Opt. Lett. 18, 846–848 (1993)

    Article  Google Scholar 

  4. Belaid, S., Lebrun, D., Ozkul, C.: Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame. Opt. Eng. 36, 1947–1951 (1997)

    Article  Google Scholar 

  5. Kreis, T.M.: Handbook of Holographic Interferometry. Wiley, Colorado (2005)

    Google Scholar 

  6. Schnars, U., Juptner, W.P.O.: Digital Holography. Springer, Berlin (2004)

    Google Scholar 

  7. Coetmellec, S., Lebrun, D., Ozkul, C.: Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform. App. Optics 41, 312–319 (2002)

    Article  Google Scholar 

  8. Xu, W., Jericho, M.H., Kreuzer, H.J.: Tracking particles if four dimensions with in-line holographic microscopy. Opt. Lett. 28, 164–166 (2003)

    Article  Google Scholar 

  9. Bragg, W., Roger, G.: Elimination of the unwanted image in diffraction microscopy. Nature 167, 190 (1951)

    Article  Google Scholar 

  10. Leith, E., Upatnieks, J.: Wavefront reconstruction with continuous-tone objects. J. Opt. Soc. Am. 53, 13771381 (1963)

    Article  Google Scholar 

  11. Cuche, E., Marquet, P., Depeursinge, C.: Spatial filtering for zero-order and twin-image elimination in digital off-axis holography. Appl. Opt. 39, 40704075 (2000)

    Article  Google Scholar 

  12. Yamaguchi, I., Zhang, T.: Phase-shifting digital holography. Opt. Lett. 22, 1268 (1997)

    Article  Google Scholar 

  13. Onural, L., Scott, P.: Digital decoding of in-line holograms. Opt. Eng. 26, 11241132 (1987)

    Article  Google Scholar 

  14. Latychevskaia, T., Fink, H.: Solution to the twin image problem in holography. Phys. Rev. Lett. 98, 23390 (2007)

    Article  Google Scholar 

  15. Denis, L., Fournier, C., Fournel, T., Ducottet, C.: Twin-image noise reduction by phase retrieval in in-line digital holography. Proc. SPIE 5914, 59140J1 (2007)

    Google Scholar 

  16. Pedrini, J., Frning, P., Fessler, H., Tiziani, H.: In-line digital holographic interferometry. Appl. Opt. 37, 62626269 (1998)

    Article  Google Scholar 

  17. Hattay, J., Belaid, S., Naanaa, W.: Geometric blind source separation using adaptive lifting scheme. In: 17th IEEE SPA conference SPA’2013 Spetember 2013 Poland

  18. Naanaa, Wady, Nuzillard, Jean-Marc: A geometric approach to blind separation of nonnegative and dependent source signals. Signal Process. 92(11), 2775–2784 (2012)

    Article  Google Scholar 

  19. Slimani, F., Grhan, G., Gouesbet, G., Allano, D.: Near-field Lorenz–Mie theory and its application to microholography. App. Optics 23(22), 4140–4148 (1984)

    Article  Google Scholar 

  20. Khosravy, M., Asharif, M.R., Yamashita, K.: A theoretical discussion on the foundation of Stones blind source separation. Signal, Image and Video Process. 5(3), 379–388 (2011)

    Article  Google Scholar 

  21. Amari, S. I., Cichocki, A., Yang, H.H.: A new learning algorithm for blind source separation, Advances in Neural Information Processing Systems 8, pp. 757–763, MIT Press (1996)

  22. Hyvarinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, Colorado (2001)

    Book  Google Scholar 

  23. Han, X.-H., Chen, Y.-W.: A robust method based on ICA and mixture sparsity for edge detection in medical images. Signal, Image and Video Process. 5(1), 39–47 (2011)

    Article  Google Scholar 

  24. Hyvarinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Comput. 9(7), 1483–1492 (1997)

    Article  Google Scholar 

  25. Chan, T.-H., Ma, W.-K., Chi, C.-Y., Wang, Y.: A convex analysis framework for blind separation of non-negative sources. IEEE Trans. Signal Process. 56, 5120–5134 (2008)

  26. Li, X., Cui, J., Zhao, L.: Blind nonlinear hyperspectral unmixing based on constrained kernel nonnegative matrix factorization. Signal, Image and Video Process. (2012). doi:10.1007/s11760-012-0392-3

  27. Ma, L., Tsoi, A.C.: A unified balanced approach to multichannel blind deconvolution. Signal, Image and Video Process. 1(4), 369–384 (2007)

    Article  MATH  Google Scholar 

  28. Smaragdis, P.: Blind separation of convolved mixtures in frequency domain. Neurocomputing 22, 21–34 (1998)

    Article  MATH  Google Scholar 

  29. Mitianoudis, N., Davies, M.: New fixed-point ICA algorithm for convolved mixtures. In: Proceedings of the 3rd International Workshop on Independent Component Analysis and Blind Source Separation, San Diego, California, pp. 633–638 (2001)

  30. Zibulevsky, M., Pearlmutter, B. A., Bofill, P., Kisilev, P.: Blind Source Separation by Sparse Decomposition, chapter in the book: S. J. Roberts, and R.M. Everson (eds.), Independent Component Analysis: Principles and Practice, Cambridge (2001)

  31. Calderbank, A.R., Daubechies, I., Sweldens, W., Yeo, B.-L.: Wavelet transforms that map integers to integers. Appl. Comput. Harmonic Anal. 5, 332–369 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  32. Hattay, J., Benazza-Benyahia, A., Pesquet, J.-C.: Adaptive lifting for multicomponent image coding through quadtree partitioning. In: Proc. of the IEEE Int. Conf. on Acoustics, Speech, Signal Processing, Philadelphia, USA (2005)

  33. Benazza-Benyahia, A., Pesquet, J.-C., Hattay, J., Masmoudi, H.: Blockbased adaptive vector lifting schemes for multichannel image coding. Eurasip Int. J. Image and Video Process. (IJIVP) 2007(1) (2007) article ID 13421, p. 10

  34. Motzkin, T., Raiffa, H., Thompson, G., Thrall, R.J.: The Double Description Method. Annals of Math Studies, 8, pp. 51–73. Princeton University Press, Princeton (1953)

    Google Scholar 

  35. Cochran, D., Gish, H., Sinno, D.: A geometric approach to multiple-channel signal detection. IEEE Trans. on Signal Process. 43(9), 2049–2057 (1995)

    Article  Google Scholar 

  36. Donoho, D.: Denoising by soft thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  37. Lebrun, D., Allano, D., Ms, L., Walle, F., Corbin, F., Boucheron, R., Frchou, D.: Size measurement of bubbles in a cavitation tunnel by digital in-line holography App. Optics 50(34), H1–H9 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jamel Hattay.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hattay, J., Belaid, S., Lebrun, D. et al. Digital in-line particle holography: twin-image suppression using sparse blind source separation. SIViP 9, 1767–1774 (2015). https://doi.org/10.1007/s11760-014-0646-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-014-0646-3

Keywords

Navigation