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

Optics Express

Volumn 20, Issue 15, 2012, Pages 17250-17257

  Memmolo, P ^a,b   Esnaola, I ^c   Finizio, A ^a   Paturzo, M ^a   Ferraro, P ^a   Tulino, A M ^b,c  

^a ISTITUTO NAZIONALE DI OTTICA   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER GENERATED HOLOGRAPHY; HOLOGRAPHIC DISPLAYS; LIGHT MODULATORS;

DE-NOISING; DENOISING METHODS; DIGITAL HOLOGRAMS; DIGITAL HOLOGRAPHY; FULL-DIGITAL; NOISE COMPONENTS; NOISE STATISTICS; PRIOR KNOWLEDGE; ROBUST METHODS; SPATIAL LIGHT MODULATORS; SPECKLE NOISE; UNCORRELATED NOISE;

HOLOGRAMS;

EID: 84864136856     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.20.017250     Document Type: Article

References (37)

1. U. Schnars and W. Jptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
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).
3. B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 610-612 (2000).
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. Express 18, 8806-8815 (2010).
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. A 24, 1617-1622 (2007).
6. D. Donoho, "De-Noising by soft thresholding," IEEE Trans. Inf. Theory 38(2), 613-627 (1995).
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).
8. J. Garcia-Sucerquia, J. A. H. Ramirez, and D. V. Prieto, "Reduction of speckle noise in digital holography by using digital image processing," Optik 116, 44-48 (2005).
9. B. Javidi, P. Ferraro, S. Hong, D. Alfieri, "Three-dimensional image fusion using multi-wavelengths digital holography," Opt. Lett. 30(2), 144-146 (2005).
10. C. Do and B. Javidi, "Three-dimensional computational holographic imaging and recognition using independent component analysis," Proc. R. Soc. London 464, 409-422 (2008).
11. M. Elad, M.A.T. Figueiredo, and M. Yi , "On the role of sparse and redundant representations in image processing," Proc. IEEE 98(6), 972-982 (2010).
12. D. Donoho, Y. Tsaig, I. Drori, 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. Theory 52(4), 1289-1306 (2006).
14. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52(2), 1289-1306 (2006).
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. A 21, 737-750 (2004).
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. A 21, 2283-2291 (2004).
19. E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, "Digital holography at 10.6 ?m," Opt. Commun. 215, 257-262 (2003).
20. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2004).
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).
23. J. Haupt, W. Bajwa, M. Rabbat, and R. Nowak, "Compressed sensing for networked data," IEEE Signal Processing Mag. 25(2), 92-101 (2008).
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 frequencyshifting holography," Opt. Lett. 35, 871-873 (2010).
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).
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).
29. Y. Rivenson, A. Stern, and B. Javidi, "Compressive Fresnel holography," J. Disp. Technol. 6(10), 506-509 (2010).
30. R. Horisaki, J. Tanida, A. Stern, and B. Javidi, "Multi-dimensional imaging using compressive Fresnel holography," Opt. Lett. 37(11), 2013-2015 (2012).
31. T. Weissman, E. Ordentlich, G. Seroussi, S. Verdú, and M. Weinberger, "Universal discrete denoising: known channel," IEEE Trans. Inf. Theory 51(1), 5-28 (2005).
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. Theory 51(12), 4203-4215 (2005).
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).
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).
36. L. I. Rudin, S. Osher and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
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).