Abstract

This paper discusses on a quantitative comparison of the performances of different advanced algorithms for phase data de-noising. In order to quantify the performances, several criteria are proposed: the gain in the signal-to-noise ratio, the Q index, the standard deviation of the phase error, and the signal to distortion ratio. The proposed methodology to investigate de-noising algorithms is based on the use of a realistic simulation of noise-corrupted phase data. A database including 25 fringe patterns divided into 5 patterns and 5 different signal-to-noise ratios was generated to evaluate the selected de-noising algorithms. A total of 34 algorithms divided into different families were evaluated. Quantitative appraisal leads to ranking within the considered criteria. A fairly good correlation between the signal-to-noise ratio gain and the quality index has been observed. There exists an anti-correlation between the phase error and the quality index which indicates that the phase errors are mainly structural distortions in the fringe pattern. Experimental results are thoroughly discussed in the paper.

© 2016 Optical Society of America

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References

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  1. T. C. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer-Verlag, New York, 2010).
  2. P. Picart, New Techniques in Digital Holography (ISTE-Wiley, London, 2015).
  3. J.W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, Greenwood Village, 2006).
  4. J. Poittevin, P. Picart, C. Faure, F. Gautier, and C. Pézerat, “Multi-point vibrometer based on high-speed digital in-line holography,” Appl. Opt. 54(11), 3185–3196 (2015).
    [Crossref] [PubMed]
  5. J. Poittevin, P. Picart, F. Gautier, and C. Pézerat, “Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology,” Opt. Express 23(24), 30917–30932 (2015).
    [Crossref] [PubMed]
  6. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
    [Crossref]
  7. Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
    [Crossref]
  8. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, New York, 1998)
  9. Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
    [Crossref]
  10. U. Schnars and W. Jüptner, “Direct Recording of Holograms by a CCD Target and Numerical Reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
    [Crossref] [PubMed]
  11. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital Holography for Quantitative Phase Contrast Imaging,” Opt. Lett. 24(5), 291–293 (1999).
    [Crossref] [PubMed]
  12. X. Chen, C. Tang, W. Xu, Y. Su, and K. Su, “General construction of transform-domain filters, filtering methods for electronic speckle pattern interferometry, and comparative analyses,” Appl. Opt. 55(9), 2214–2222 (2016).
    [Crossref] [PubMed]
  13. A. Frederico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40(11), 2598–2604 (2001).
    [Crossref]
  14. T. Asakura, “Surface roughness measurements,” in Speckle Metrology, R. K. Erf, ed., pp. 11–49 (Academic Press, New York, 1978).
  15. Z. Wang, A. C. Bovik, and L. Lu, “Why is image quality assessment so difficult?” Proc. IEEE ICASSP4, 3313–3316 (2002).
    [Crossref]
  16. A. Federico and G. H. Kaufmann, “Denoising in digital speckle pattern interferometry using wave atoms,” Opt. Lett. 32(10), 1232–1234 (2007).
    [Crossref] [PubMed]
  17. 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(15), 17250–17257 (2012).
    [Crossref]
  18. T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45(24), 6077–6085 (2006).
    [Crossref] [PubMed]
  19. L. Rong, W. Xiao, F. Pan, S. Liu, and R. Li, “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010).
    [Crossref]
  20. V. Bianco, M. Paturzo, P. Memmolo, A. Finizio, P. Ferraro, and B. Javidi, “Random resampling masks: a non-Bayesian one-shot strategy for noise reduction in digital holography,” Opt. Lett. 38(5), 619–621 (2013).
    [Crossref] [PubMed]
  21. R. C. Gonzales and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, Upper Saddle River, 2008).
  22. J. S. Lee, ““Digital image enhancement and noise filtering by using local statistics,” IEEE Trans. on Patt,” Anal. And Mach. Intell. 2, 165–1658 (1980).
    [Crossref]
  23. V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
    [Crossref]
  24. S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, New York, 1999).
  25. D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41(3), 613–627 (1995).
    [Crossref]
  26. H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
    [Crossref]
  27. J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
    [Crossref] [PubMed]
  28. M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
    [Crossref] [PubMed]
  29. G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35(1), 9–14 (1996).
    [Crossref]
  30. A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
    [Crossref]
  31. A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
    [Crossref]
  32. A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
    [Crossref]
  33. A. Uzan, Y. Rivenson, and A. Stern, “Speckle denoising in digital holography by nonlocal means filtering,” Appl. Opt. 52(1), A195–A200 (2013).
    [Crossref] [PubMed]
  34. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
    [Crossref]
  35. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
    [Crossref] [PubMed]
  36. V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
    [Crossref]
  37. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
    [Crossref] [PubMed]
  38. L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
    [Crossref]
  39. Q. Kemao, T. H. Nam, L. Feng, and S. H. Soon, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46(30), 7412–7418 (2007).
    [Crossref] [PubMed]
  40. Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45(12), 1186–1192 (2007).
    [Crossref]
  41. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
    [Crossref]
  42. P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “Quantitative phase maps denoising of long holographic sequences by using SPADEDH algorithm,” Appl. Opt. 52(7), 1453–1460 (2013).
    [Crossref] [PubMed]
  43. V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi and P. Ferraro, “Quasi noise-free digital holography,” Light Science & Applications, accepted article preview 31 March 2016.
  44. M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
    [Crossref]

2016 (1)

2015 (2)

2013 (3)

2012 (2)

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

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(15), 17250–17257 (2012).
[Crossref]

2010 (3)

L. Rong, W. Xiao, F. Pan, S. Liu, and R. Li, “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010).
[Crossref]

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

2007 (5)

Q. Kemao, T. H. Nam, L. Feng, and S. H. Soon, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46(30), 7412–7418 (2007).
[Crossref] [PubMed]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45(12), 1186–1192 (2007).
[Crossref]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

A. Federico and G. H. Kaufmann, “Denoising in digital speckle pattern interferometry using wave atoms,” Opt. Lett. 32(10), 1232–1234 (2007).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

2006 (3)

T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45(24), 6077–6085 (2006).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

2005 (4)

A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
[Crossref]

A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
[Crossref]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

2004 (1)

2003 (1)

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

2002 (2)

H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
[Crossref]

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[Crossref] [PubMed]

2001 (1)

A. Frederico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40(11), 2598–2604 (2001).
[Crossref]

1999 (2)

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital Holography for Quantitative Phase Contrast Imaging,” Opt. Lett. 24(5), 291–293 (1999).
[Crossref] [PubMed]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

1996 (1)

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35(1), 9–14 (1996).
[Crossref]

1995 (1)

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41(3), 613–627 (1995).
[Crossref]

1994 (1)

1982 (1)

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

1980 (1)

J. S. Lee, ““Digital image enhancement and noise filtering by using local statistics,” IEEE Trans. on Patt,” Anal. And Mach. Intell. 2, 165–1658 (1980).
[Crossref]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Astola, J.

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

Asundi, A.

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Baumbach, T.

Bevilacqua, F.

Bianco, V.

Bovik, A. C.

Z. Wang, A. C. Bovik, and L. Lu, “Why is image quality assessment so difficult?” Proc. IEEE ICASSP4, 3313–3316 (2002).
[Crossref]

Buades, A.

A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
[Crossref]

A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
[Crossref]

Candès, E. J.

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[Crossref] [PubMed]

Chen, X.

Coll, B.

A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
[Crossref]

A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
[Crossref]

Cuche, E.

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

Depeursinge, C.

Do, M. N.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

Donoho, D. L.

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[Crossref] [PubMed]

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41(3), 613–627 (1995).
[Crossref]

Egiazarian, K.

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

Esnaola, I.

Faure, C.

Federico, A.

Feng, L.

Ferraro, P.

Finizio, A.

Foi, A.

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

Frederico, A.

A. Frederico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40(11), 2598–2604 (2001).
[Crossref]

Frost, V. S.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

Galizzi, G. E.

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35(1), 9–14 (1996).
[Crossref]

Gautier, F.

Gotchev, A.

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

Holtzman, J. C.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

Huang, L.

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Iannone, M.

Javidi, B.

Jüptner, W.

Karray, M.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

Katkovnik, V.

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

Kaufmann, G. H.

A. Federico and G. H. Kaufmann, “Denoising in digital speckle pattern interferometry using wave atoms,” Opt. Lett. 32(10), 1232–1234 (2007).
[Crossref] [PubMed]

A. Frederico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40(11), 2598–2604 (2001).
[Crossref]

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35(1), 9–14 (1996).
[Crossref]

Kebbel, V.

Kemao, Q.

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45(12), 1186–1192 (2007).
[Crossref]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

Q. Kemao, T. H. Nam, L. Feng, and S. H. Soon, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46(30), 7412–7418 (2007).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Kolenovic, E.

Lee, J. S.

J. S. Lee, ““Digital image enhancement and noise filtering by using local statistics,” IEEE Trans. on Patt,” Anal. And Mach. Intell. 2, 165–1658 (1980).
[Crossref]

Li, R.

Liu, S.

Lu, L.

Z. Wang, A. C. Bovik, and L. Lu, “Why is image quality assessment so difficult?” Proc. IEEE ICASSP4, 3313–3316 (2002).
[Crossref]

Memmolo, P.

Morel, J.

A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
[Crossref]

Morel, J. M.

A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
[Crossref]

Nam, T. H.

Netti, P. A.

Pan, B.

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Pan, F.

Paturzo, M.

Pézerat, C.

Picart, P.

Pierce, L. E.

H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
[Crossref]

Poittevin, J.

Rivenson, Y.

Rong, L.

Roussev, I. R.

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

Schnars, U.

Shanmugan, K. S.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

Shulev, A. A.

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

Slangen, P.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

Soon, S. H.

Q. Kemao, T. H. Nam, L. Feng, and S. H. Soon, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46(30), 7412–7418 (2007).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Starck, J.-L.

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[Crossref] [PubMed]

Stern, A.

Stiles, J. A.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

Su, K.

Su, Y.

Tang, C.

Tulino, A. M.

Ulaby, F. T.

H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
[Crossref]

Uzan, A.

Ventre, M.

Vetterli, M.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, and L. Lu, “Why is image quality assessment so difficult?” Proc. IEEE ICASSP4, 3313–3316 (2002).
[Crossref]

Xiao, W.

Xie, H.

H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
[Crossref]

Xu, W.

Anal. And Mach. Intell. (1)

J. S. Lee, ““Digital image enhancement and noise filtering by using local statistics,” IEEE Trans. on Patt,” Anal. And Mach. Intell. 2, 165–1658 (1980).
[Crossref]

Appl. Opt. (8)

U. Schnars and W. Jüptner, “Direct Recording of Holograms by a CCD Target and Numerical Reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
[Crossref] [PubMed]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[Crossref] [PubMed]

T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45(24), 6077–6085 (2006).
[Crossref] [PubMed]

Q. Kemao, T. H. Nam, L. Feng, and S. H. Soon, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46(30), 7412–7418 (2007).
[Crossref] [PubMed]

A. Uzan, Y. Rivenson, and A. Stern, “Speckle denoising in digital holography by nonlocal means filtering,” Appl. Opt. 52(1), A195–A200 (2013).
[Crossref] [PubMed]

P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “Quantitative phase maps denoising of long holographic sequences by using SPADEDH algorithm,” Appl. Opt. 52(7), 1453–1460 (2013).
[Crossref] [PubMed]

J. Poittevin, P. Picart, C. Faure, F. Gautier, and C. Pézerat, “Multi-point vibrometer based on high-speed digital in-line holography,” Appl. Opt. 54(11), 3185–3196 (2015).
[Crossref] [PubMed]

X. Chen, C. Tang, W. Xu, Y. Su, and K. Su, “General construction of transform-domain filters, filtering methods for electronic speckle pattern interferometry, and comparative analyses,” Appl. Opt. 55(9), 2214–2222 (2016).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

Exp. Mech. (1)

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (1)

H. Xie, L. E. Pierce, and F. T. Ulaby, “Sar speckle reduction using wavelet denoising and markov random field modeling,” IEEE Trans. Geosci. Rem. Sens. 40(10), 2196–2212 (2002).
[Crossref]

IEEE Trans. Image Process. (3)

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[Crossref] [PubMed]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41(3), 613–627 (1995).
[Crossref]

IEEE Trans. Patt. Anal. And Mach. Intell PAMI (1)

V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Patt. Anal. And Mach. Intell PAMI 4(2), 157–166 (1982).
[Crossref]

Int. J. Comput. Vis. (1)

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” Int. J. Comput. Vis. 86(1), 1–32 (2010).
[Crossref]

Multiscale Model. Simul. (1)

A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005).
[Crossref]

Opt. Commun. (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Opt. Eng. (2)

A. Frederico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40(11), 2598–2604 (2001).
[Crossref]

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35(1), 9–14 (1996).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (2)

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Opt. Lasers Eng. (3)

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45(12), 1186–1192 (2007).
[Crossref]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[Crossref]

Opt. Lett. (3)

Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. (1)

A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 2(2), 60–65 (2005).
[Crossref]

Proc. SPIE (2)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 606414 (2006).
[Crossref]

A. A. Shulev, A. Gotchev, A. Foi, and I. R. Roussev, “Threshold selection in transform-domain denoising of speckle pattern fringes,” Proc. SPIE 6252, 625220 (2006).
[Crossref]

Other (9)

S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, New York, 1999).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, New York, 1998)

T. C. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer-Verlag, New York, 2010).

P. Picart, New Techniques in Digital Holography (ISTE-Wiley, London, 2015).

J.W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, Greenwood Village, 2006).

T. Asakura, “Surface roughness measurements,” in Speckle Metrology, R. K. Erf, ed., pp. 11–49 (Academic Press, New York, 1978).

Z. Wang, A. C. Bovik, and L. Lu, “Why is image quality assessment so difficult?” Proc. IEEE ICASSP4, 3313–3316 (2002).
[Crossref]

R. C. Gonzales and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, Upper Saddle River, 2008).

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi and P. Ferraro, “Quasi noise-free digital holography,” Light Science & Applications, accepted article preview 31 March 2016.

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Figures (13)

Fig. 1
Fig. 1 plots of the probability density function vs different values of |μ|.
Fig. 2
Fig. 2 Arrangement to produce speckle phase decorrelation in phase change due to surface deformation.
Fig. 3
Fig. 3 Examples of outputs from the numerical simulation, (a) surface deformation in radians, (b) modulo 2π noisy phase map including the speckle phase decorrelation, (c) autocorrelation of the speckle intensity providing the size of the speckle grain, (d) decorrelation noise, (e) probability density of the decorrelation noise (red: theoretical Eq. (4), blue: obtained from Fig. 3(d), and 3(f) cosine image of the noisy phase, the signal-to-noise ratio in this image is 5.08dB.
Fig. 4
Fig. 4 Outputs from the numerical simulation for 5 different values of the SNR, respectively for each row at 7.31dB, 6.10dB, 5.08dB, 4.03dB and 3.10dB, (a),(f),(k),(p),(u) respectively the cosine of the noisy phase, (b),(g),(l),(q),(v) the sine of the noisy phase, (c),(h),(m),(r),(w) the modulo 2π deformation phase maps, (d),(i),(n),(s),(x) the modulo 2π noisy deformation phase maps, and (e),(j),(o),(t),(y) the noise maps extracted from the simulation.
Fig. 5
Fig. 5 Outputs from the numerical simulation for 5 different fringe patterns, (a) to (e): cosine of the simulated phase, (f) to (j): cosine of the noisy phase for SNR at respectively 3.10dB, 3.59dB, 3.34dB, 3.66dB and 3.65 dB (average value at 3.46dB), (k) to (o): simulated modulo 2π deformation phase maps, (p) to (t): modulo 2π noisy deformation phase maps, (u) to (y): noise maps.
Fig. 6
Fig. 6 (a) results obtained for the average value of σφ, (b) results obtained for the signal to noise ratio gain, (c) ranking obtained for Qindex, (d) ranking obtained for SDR, (e) evolution of the average value of σφ according to the input signal to noise ratio, (f) detail of the performance with the SNR gain according to the input SNR, (g) performance of the selected methods regarding to the Qindex, (h) performance of the selected methods according to the SDR.
Fig. 7
Fig. 7 Correlations between the four indices, (a) correlation between phase error and the cosine Qindex., (b) correlation between GSNR and Qindex., (c) correlation between GSNR and σφ., (d) correlation between SDR and σφ.
Fig. 8
Fig. 8 Trends for the standard deviation of the phase error, σφ, versus the input SNR for the 20 selected methods.
Fig. 9
Fig. 9 Trends for GSNR of cosine image versus the input SNR for the 20 selected methods.
Fig. 10
Fig. 10 Trends for Qindex versus the input SNR for the 20 selected methods.
Fig. 11
Fig. 11 Trends for SDR versus the input SNR for the 20 selected methods.
Fig. 12
Fig. 12 De-noising of the 1st fringe pattern of Fig. 5 (1st column), (a) processing with BM3D, (b) corresponding residual noise, (c) processing with curvelets, (d) corresponding residual noise, (e) processing with NLmeans (7,15,30), (f) corresponding residual noise, (g) 9 × 9 median, (h) corresponding residual noise, (i) WFT2F, (j) corresponding residual noise, (k) Daubechie 8, (l) corresponding residual noise.
Fig. 13
Fig. 13 Experimental phase processed with WFT2F, (a) noisy phase map, (b) filtered phase map using WFT2F, (c) residual noise estimated from the processing.

Equations (12)

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H= | R | 2 + | O | 2 + R * O+R O * .
O( x,y, d 0 )= i λ d 0 exp( 2iπ d 0 λ )exp( iπ λ d 0 ( x 2 + y 2 ) ) × A ( X,Y )exp( iπ λ d 0 ( X 2 + Y 2 ) )exp( 2iπ λ d 0 ( xX+yY ) )dXdY .
A r ( X,Y, d 0 )= iexp( 2iπ d 0 /λ ) λ d 0 exp[ iπ λ d 0 ( X 2 + Y 2 ) ] × k l H( l p x ,k p y , d 0 ) exp[ iπ λ d 0 ( l 2 p x 2 + k 2 p y 2 ) ]exp[ 2iπ λ d 0 ( lX p x +kY p y ) ].
p( ε )= 1 | μ | 2 2π ( 1 β 2 ) 3/2 ( β sin 1 β+ πβ 2 + 1 β 2 ).
PSF( X,Y )= i λf exp( 2iπf λ )exp( iπ λf ( X 2 + Y 2 ) ) × p ( x',y' )exp( 2iπ λf ( x'X+y'Y ) )dx'dy' .
G SNR = R SNR I SNR .
R SNR =10 log 10 [ i,j s 2 ( i,j ) i,j [ s( i,j )d( i,j ) ] 2 ].
Q index = σ sd σ s σ d 2 μ s μ d μ s 2 + μ d 2 2 σ s σ d σ s 2 + σ d 2 .
σ ϕ = ε ϕ 2 ε ϕ 2 .
SDR= s 2 sd 2 .
W( u,v )= H( u,v ) Φ s ( u,v ) | H( u,v ) | 2 Φ s ( u,v )+ Φ b ( u,v ) .
d( x,y )=αs( x,y )+( 1α μ s ).

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