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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 17250–17257

SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics

P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino  »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 17250-17257 (2012)

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In this paper we propose a robust method to suppress the noise components in digital holography (DH), called SPADEDH (SPArsity DEnoising of Digital Holograms), that does not consider any prior knowledge or estimation about the statistics of the noise. In the full digital holographic process we must mainly deal with two kinds of noise. The first one is an additive uncorrelated noise that corrupts the observed irradiance, the other one is the multiplicative phase noise called speckle noise. We consider both lensless and microscope configurations and we prove that the proposed algorithm works efficiently in all considered cases suppressing the aforementioned noise components. In addition, for digital holograms recorded in lensless configuration, we show the improvement in a display test by using a Spatial Light Modulator (SLM).

© 2012 OSA

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.3010) Image processing : Image reconstruction techniques
(090.1995) Holography : Digital holography

ToC Category:

Original Manuscript: February 27, 2012
Revised Manuscript: June 4, 2012
Manuscript Accepted: June 4, 2012
Published: July 13, 2012

P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, "SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics," Opt. Express 20, 17250-17257 (2012)

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  1. U. Schnars and W. Jptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt.33, 179–181 (1994). [CrossRef] [PubMed]
  2. P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett.31, 1405–1407 (2006). [CrossRef] [PubMed]
  3. B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett.25, 610–612 (2000). [CrossRef]
  4. M. Paturzo, P. Memmolo, A. Finizio, R. Nsnen, T.J. Naughton, and P. Ferraro, “Synthesis and display of dynamic holographic 3D scenes with real-world objects,” Opt. Express18, 8806–8815 (2010). [CrossRef] [PubMed]
  5. J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A24, 1617–1622 (2007). [CrossRef]
  6. D. Donoho, “De-Noising by soft thresholding,” IEEE Trans. Inf. Theory38(2), 613–627 (1995). [CrossRef]
  7. S. Mirza, R. Kumar, and C. Shakher, “Study of various preprocessing schemes and wavelet filters for speckle noise reduction in digital speckle pattern interferometric fringes,” Opt. Eng.44(4), 045603, (2005). [CrossRef]
  8. J. Garcia-Sucerquia, J. A. H. Ramirez, and D. V. Prieto, “Reduction of speckle noise in digital holography by using digital image processing,” Optik116, 44–48 (2005). [CrossRef]
  9. B. Javidi, P. Ferraro, S. Hong, and D. Alfieri, “Three-dimensional image fusion using multi-wavelengths digital holography,” Opt. Lett.30(2), 144–146 (2005). [CrossRef] [PubMed]
  10. C. Do and B. Javidi, “Three-dimensional computational holographic imaging and recognition using independent component analysis,” Proc. R. Soc. London464, 409–422 (2008). [CrossRef]
  11. M. Elad, M.A.T. Figueiredo, and M. Yi, “On the role of sparse and redundant representations in image processing,” Proc. IEEE98(6), 972–982 (2010). [CrossRef]
  12. D. Donoho, Y. Tsaig, I. Drori, and J-L Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Stanford Technical Report 1–39 (2006).
  13. D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006). [CrossRef]
  14. E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52(2), 1289–1306 (2006). [CrossRef]
  15. A.M. Tulino, G. Caire, S. Shamai, and S. Verdú, “Support recovery with sparsely sampled free random matrices,” The IEEE International Symposium on Information Theory (ISIT 2011), Saint-Petersburg, Russia, July, 31–August, 5, (2011).
  16. Y. Wu, “Shannon theory for compressed sensing,” Ph. D. dissertation, Princeton University, Sep. (2011).
  17. S. Sotthivirat and J. A. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A21, 737–750 (2004). [CrossRef]
  18. N. Bertaux, Y. Frauel, P. Rfrgier, and B. Javidi, “Speckle removal using a maximum-likelihood technique with isoline gray-level regularization,” J. Opt. Soc. Am. A21, 2283–2291 (2004). [CrossRef]
  19. E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, “Digital holography at 10.6 μm,” Opt. Commun.215, 257–262 (2003). [CrossRef]
  20. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2004). [CrossRef]
  21. M. Lustig, J. Santos, J. Lee, D. Donoho, and J. Pauly, “Application of compressed sensing for rapid MR imaging,” In Proc. Work. Struc. Parc. Rep. Adap. Signaux (SPARS), Rennes, France, Nov. (2005).
  22. M. Mishali and Y. C. Eldar, “From theory to practice: sub-Nyquist sampling of sparse wideband analog signals,” IEEE J. Sel. Top. Signal Process.4(2), 375–391 (2010). [CrossRef]
  23. J. Haupt, W. Bajwa, M. Rabbat, and R. Nowak, “Compressed sensing for networked data,” IEEE Signal Processing Mag.25(2), 92–101 (2008). [CrossRef]
  24. R. Marcia, Z. Harmany, and R. Willett, “Compressive coded aperture imaging,” In Proc. IS&T/SPIE Symp. Elec. Imag.: Comp. Imag., San Jose, CA, (2009).
  25. A. Majumdar and R.K. Ward, “Sparsity promoting speckle denoising,” International Conference on Image Processing (2009).
  26. M. M. Marim, M. Atlan, E. Angelini, and J-C Olivo-Marin, “Compressed sensing with off-axis frequency-shifting holography,” Opt. Lett.35, 871–873 (2010). [CrossRef] [PubMed]
  27. M. M. Marim, E. Angelini, J-C Olivo-Marin, and M. Atlan, “Off-axis compressed holographic microscopy in low-light conditions,” Opt. Lett.36, 79–81 (2011). [CrossRef] [PubMed]
  28. K. Choi, R. Horisaki, J. Hahn, S. Lim, D.L. Marks, T.J. Schulz, and D.J. Brady, “Compressive holography of diffuse objects,” Appl. Opt.49, H1–H10 (2010). [CrossRef] [PubMed]
  29. Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol.6(10), 506–509 (2010). [CrossRef]
  30. R. Horisaki, J. Tanida, A. Stern, and B. Javidi, “Multi-dimensional imaging using compressive Fresnel holography,” Opt. Lett.37(11), 2013–2015 (2012). [CrossRef] [PubMed]
  31. T. Weissman, E. Ordentlich, G. Seroussi, S. Verdú, and M. Weinberger, “Universal discrete denoising: known channel,” IEEE Trans. Inf. Theory51(1), 5–28 (2005). [CrossRef]
  32. S. Rangan, A.K. Fletcher, and V.K. Goyal, “Asymptotic analysis of MAP estimation via the replica method and applications to compressed sensing,” http://www.citebase.org/abstract?id=oai:arXiv.org:0906.3234 , (2009).
  33. E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory51(12), 4203–4215 (2005). [CrossRef]
  34. A. Pelagotti, M. Locatelli, A.G. Geltrude, P. Poggi, R. Meucci, M. Paturzo, L. Miccio, and P. Ferraro, “Reliability of 3D imaging by digital holography at long IR wavelength,” J. Disp. Technol.6, 465–471 (2010). [CrossRef]
  35. P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett.84, 2709–2711 (2004). [CrossRef]
  36. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D60, 259–268 (1992). [CrossRef]
  37. P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, “Automatic focusing in digital holography and its application to stretched holograms,” Opt. Lett.36, 1945–1947 (2011). [CrossRef] [PubMed]

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