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

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

http://dx.doi.org/10.1364/OE.20.017250

Acrobat PDF (719 KB)

### Abstract

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

## 1. Introduction

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. Express **18**, 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. A **24**, 1617–1622 (2007). [CrossRef]

6. D. Donoho, “De-Noising by soft thresholding,” IEEE Trans. Inf. Theory **38**(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,” Optik **116**, 44–48 (2005). [CrossRef]

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). [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. London **464**, 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. IEEE **98**(6), 972–982 (2010). [CrossRef]

13. D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory **52**(4), 1289–1306 (2006). [CrossRef]

17. S. Sotthivirat and J. A. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A **21**, 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. A **21**, 2283–2291 (2004). [CrossRef]

*l*

_{1}minimization algorithm, solved by StOMP, which is able to suppress the noise components on digital holograms without any prior knowledge or estimation about the statistics of noise. We have tested the SPADEDH method to various types of digital holograms, using different objects, from microscopic to macroscopic size, recorded in different conditions and with different wavelengths (either in visible as well as in IR spectrum [19

19. E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, “Digital holography at 10.6 *μ*m,” Opt. Commun. **215**, 257–262 (2003). [CrossRef]

## 2. Noise model

*H*is formed in the interference plane: where

*O*is the diffracted field produced by the object and

*R*is the reference. With a simple mathematical manipulation, we can rewrite the Eq. (1) as follow: where The quantity

*q*is called zero-order diffraction term, while the contribution in Eq. (2) contains both +1 and −1 diffraction orders. The hologram

*H*is recorded by a CCD and it is usually corrupted by a mixture of speckle noise and additive noise described by Eq. (2): where

*n*and

_{s}*n*are speckle noise, modeled by a multiplicative uniform noise, and an additive zero mean Gaussian noise respectively. The numerical process produces a digital version of the hologram that is reconstructed using a numerical version of the diffraction integral [20

_{a}20. T. Kreis, *Handbook of Holographic Interferometry: Optical and Digital Methods* (Wiley-VCH, 2004). [CrossRef]

20. T. Kreis, *Handbook of Holographic Interferometry: Optical and Digital Methods* (Wiley-VCH, 2004). [CrossRef]

## 3. SPADEDH algorithm

## 4. Numerical results

*μm*and a visible laser at 532

*nm*, respectively, and the hologram of a Micro Electro Mechanical System (MEMS). Basically two kinds of experimental set-ups were used to acquire these digital holograms: a lensless set-up to record the speckle holograms and a microscope configuration one to acquire MEMS hologram in reflection mode, that is necessary to acquire holograms of opaque objects as the MEMS. The lensless set-up is described in detail in [34

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]

*ℓ*

_{1}-norm of the estimated signal via StOMP, as opposed to traditional denoising approaches in which the total variation of the signal estimate is minimized [36

36. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D **60**, 259–268 (1992). [CrossRef]

*, a low complex recovery is desirable, due to the fact that each greedy step is computationally more demanding than in the traditional CS setting for which*

_{n}*m*≪

*n*. In addition to that, for

*n*large, StOMP has a performance comparable to that achievable by

*ℓ*

_{1}minimization based in linear programming. This condition holds in our setting since the dimension of

**h**̃ is large in general for images (in our case

*n*= 1024 × 1024 for the speckle hologram recorded at 532

*nm*and the MEMS hologram, while

*n*= 640 × 480 for the speckle hologram recorded at 10.6

*μm*), and further increases when we move to higher resolutions.

*, we use the in-focus distance, while for the hologram recorded in microscope configuration we use the Back Focal Plane (BFP) distance because, in this case, we have the biggest degree of sparsity in that plane. In particular, for the hologram acquired at 10.6*

_{δ}*μm*, as it is in-focus in the Fourier plane, we use

*δ*= ∞. The results of the SPADEDH algorithm are shown in Fig. 1. In all cases, the final holograms are obtained by the back propagation, of the denoised complex field

**v**

*, in the hologram plane. In order to evaluate the results, for lensless holograms, we perform also a display test, by using a SLM as a (potentially 3D) projection system (see Fig. 2), while, for the hologram recorded in microscopic configuration, we compute the amplitude in-focus reconstruction. We compare SPADEDH algorithm with the Discrete Fourier Filter (DFF) [5*

_{den}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). [CrossRef]

*N*times and the resulting

*N*intensities are summed. In our implementation of this method, we set

*N*= 100. Note that, this method is based on the perfect knowledge of the hologram bandwidth. In order to quantify the efficiency of the SPADEDH method, in terms of how much noise we are able to remove from the original reconstruction, we define two different parameters: the signal to distortion ratio (SDR) and a measure of contrast C, given in [37

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]

_{2}is the

*l*

_{2}norm, Ĩ = |F

_{δ}**h**̃| is the amplitude of the original infocus digital reconstruction and Î = |F

_{d}**h**

*| is the processed one and, in Eq. (10),*

_{den}*σ*(I) and 〈I〉 represent the image gray-level standard deviation and mean, respectively, and I is the amplitude of the in-focus digital reconstruction of original hologram in one case and in the other case is the amplitude of the processed one. In Table 1 and Table 2 we report the computation of the two parameters of efficiency for the cases under analysis.

*C*and this shows its effective efficiency and robustness with respect the variation of experimental parameters. Finally, in order to evaluate the improvement of projections in the display test, we compute the of intensity into signal regions (SR) percentage increase, shown in the Fig. 2 For the statuette of astronaut we have

*G*≈ 31%, while for the statuette of Venus results

*G*≈ 16%.

## 5. Conclusion

*l*

_{1}minimization problem, that does not consider any prior information of the noise statistics. Numerical results show the goodness and robustness of the SPADEDH algorithm for both lensless holograms of centimeters size objects at Vis as well as at long IR wavelengths and for holograms recorded in microscopic configuration, with respect the DFF technique. In the first case, the display of denoised holograms shows the improvement in terms of the efficiency of the optical reconstruction. In fact, an increasing of intensity of the reconstructed in object image was observed. Also for the holograms recorded in microscope configuration we obtained good results in terms of denoising in the BFP spectrum as well as an improvement in the reconstruction efficiency in terms of both SDR and image contrast.

## Acknowledgments

## References and links

1. | U. Schnars and W. Jptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. |

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. |

3. | B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. |

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 |

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 |

6. | D. Donoho, “De-Noising by soft thresholding,” IEEE Trans. Inf. Theory |

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. |

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 |

9. | B. Javidi, P. Ferraro, S. Hong, and D. Alfieri, “Three-dimensional image fusion using multi-wavelengths digital holography,” Opt. Lett. |

10. | C. Do and B. Javidi, “Three-dimensional computational holographic imaging and recognition using independent component analysis,” Proc. R. Soc. London |

11. | M. Elad, M.A.T. Figueiredo, and M. Yi, “On the role of sparse and redundant representations in image processing,” Proc. IEEE |

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. Theory |

14. | E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory |

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 |

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 |

19. | E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, “Digital holography at 10.6 |

20. | T. Kreis, |

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. |

23. | J. Haupt, W. Bajwa, M. Rabbat, and R. Nowak, “Compressed sensing for networked data,” IEEE Signal Processing Mag. |

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. |

27. | M. M. Marim, E. Angelini, J-C Olivo-Marin, and M. Atlan, “Off-axis compressed holographic microscopy in low-light conditions,” Opt. Lett. |

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. |

29. | Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. |

30. | R. Horisaki, J. Tanida, A. Stern, and B. Javidi, “Multi-dimensional imaging using compressive Fresnel holography,” Opt. Lett. |

31. | T. Weissman, E. Ordentlich, G. Seroussi, S. Verdú, and M. Weinberger, “Universal discrete denoising: known channel,” IEEE Trans. Inf. Theory |

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 |

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. |

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. |

36. | L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D |

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. |

**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:**

Holography

**History**

Original Manuscript: February 27, 2012

Revised Manuscript: June 4, 2012

Manuscript Accepted: June 4, 2012

Published: July 13, 2012

**Citation**

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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-17250

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### References

- U. Schnars and W. Jptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt.33, 179–181 (1994). [CrossRef] [PubMed]
- 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]
- B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett.25, 610–612 (2000). [CrossRef]
- 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]
- 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]
- D. Donoho, “De-Noising by soft thresholding,” IEEE Trans. Inf. Theory38(2), 613–627 (1995). [CrossRef]
- 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]
- 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]
- 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]
- C. Do and B. Javidi, “Three-dimensional computational holographic imaging and recognition using independent component analysis,” Proc. R. Soc. London464, 409–422 (2008). [CrossRef]
- 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]
- 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).
- D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006). [CrossRef]
- 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]
- 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).
- Y. Wu, “Shannon theory for compressed sensing,” Ph. D. dissertation, Princeton University, Sep. (2011).
- S. Sotthivirat and J. A. Fessler, “Penalized-likelihood image reconstruction for digital holography,” J. Opt. Soc. Am. A21, 737–750 (2004). [CrossRef]
- 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]
- 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]
- T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2004). [CrossRef]
- 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).
- 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]
- J. Haupt, W. Bajwa, M. Rabbat, and R. Nowak, “Compressed sensing for networked data,” IEEE Signal Processing Mag.25(2), 92–101 (2008). [CrossRef]
- 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).
- A. Majumdar and R.K. Ward, “Sparsity promoting speckle denoising,” International Conference on Image Processing (2009).
- 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]
- 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]
- 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]
- Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol.6(10), 506–509 (2010). [CrossRef]
- 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]
- 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]
- 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).
- E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory51(12), 4203–4215 (2005). [CrossRef]
- 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]
- 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]
- L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D60, 259–268 (1992). [CrossRef]
- 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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