Abstract

We propose a bidimensional empirical mode decomposition (BEMD) method to reduce speckle noise in digital speckle pattern interferometry (DSPI) fringes. The BEMD method is based on a sifting process that decomposes the DSPI fringes in a finite set of subimages represented by high and low frequency oscillations, which are named modes. The sifting process assigns the high frequency information to the first modes, so that it is possible to discriminate speckle noise from fringe information, which is contained in the remaining modes. The proposed method is a fully data-driven technique, therefore neither fixed basis functions nor operator intervention are required. The performance of the BEMD method to denoise DSPI fringes is analyzed using computer-simulated data, and the results are also compared with those obtained by means of a previously developed one-dimensional empirical mode decomposition approach. An application of the proposed BEMD method to denoise experimental fringes is also presented.

© 2008 Optical Society of America

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References

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  1. J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59-139.
  2. K. Creath, “Temporal phase method,” in Interferogram Analysis, D. Robinson and G. Reid, eds. (Institute of Physics, 1993), pp. 94-140.
  3. P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).
  4. L. Watkins, S. Tan, and T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905-907 (1999).
  5. C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182-3193 (2003).
  6. A. Federico and G. H. Kaufmann, “Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes,” Appl. Opt. 45, 1909-1916 (2006).
    [CrossRef]
  7. G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding ,” Opt. Eng. 35, 9-14 (1996).
  8. A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001).
  9. A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44, 2728-2735 (2005).
    [CrossRef]
  10. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).
  11. M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).
  12. J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).
  13. J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).
  14. G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, Grado, Italy (IEEE, 2003), http://perso.ens-lyon.fr/patrick.flandrin/publis.html#Communications.
  15. A. Linderhed, “Variable sampling of the empirical mode decomposition of two-dimensional signals,” Int. J. Wavelets Multires. Inf. Process. 3, 435-452 (2005).
  16. C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).
  17. F. L. Bookstein, “Principal warps: thin-plate splines and the decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567-585 (1989).
  18. Y. Tian, Y. Huang, and Y. Li, “Image zooming method using 2D EMD technique,” in Proceedings of IEEE 6th World Congress on Intelligent Control and Automation (IEEE, 2006), pp. 10036-10040.
  19. T. Y. Yang, Finite Element Structural Analysis (Prentice-Hall, 1986), pp. 446-449.
  20. M. Shen, H. Tang, and B. Li, “The modified bidimensional empirical mode decomposition for image denoising,” in Proceedings of IEEE 8th International Conference on Signal Processing (IEEE, 2006), pp. 16-20.
  21. S. Sinclair and G. G. S. Pegram, “Empirical mode decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting,” Hydrol. Earth Syst. Sciences 9, 127-137 (2005).
  22. P. D. Ruiz and G. H. Kaufmann, “Evaluation of a scale-space filter for speckle noise reduction in electronic speckle pattern interferometry,” Opt. Eng. 37, 2395-2401 (1998).
  23. G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010-2014 (2003).

2007 (1)

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

2006 (1)

2005 (5)

A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44, 2728-2735 (2005).
[CrossRef]

S. Sinclair and G. G. S. Pegram, “Empirical mode decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting,” Hydrol. Earth Syst. Sciences 9, 127-137 (2005).

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).

A. Linderhed, “Variable sampling of the empirical mode decomposition of two-dimensional signals,” Int. J. Wavelets Multires. Inf. Process. 3, 435-452 (2005).

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).

2003 (3)

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182-3193 (2003).

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010-2014 (2003).

2001 (1)

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001).

2000 (1)

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

1999 (1)

1998 (2)

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

P. D. Ruiz and G. H. Kaufmann, “Evaluation of a scale-space filter for speckle noise reduction in electronic speckle pattern interferometry,” Opt. Eng. 37, 2395-2401 (1998).

1996 (1)

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

1989 (1)

F. L. Bookstein, “Principal warps: thin-plate splines and the decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567-585 (1989).

Barnes, T.

Bernini, M. B.

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

Bookstein, F. L.

F. L. Bookstein, “Principal warps: thin-plate splines and the decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567-585 (1989).

Bouaoune, Y.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Bunel, P.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Creath, K.

K. Creath, “Temporal phase method,” in Interferogram Analysis, D. Robinson and G. Reid, eds. (Institute of Physics, 1993), pp. 94-140.

Damerval, C.

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).

Delechelle, E.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Deléchelle, E.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).

Federico, A.

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

A. Federico and G. H. Kaufmann, “Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes,” Appl. Opt. 45, 1909-1916 (2006).
[CrossRef]

A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44, 2728-2735 (2005).
[CrossRef]

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001).

Flandrin, P.

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, Grado, Italy (IEEE, 2003), http://perso.ens-lyon.fr/patrick.flandrin/publis.html#Communications.

Galizzi, G. E.

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

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

Gonçalves, P.

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, Grado, Italy (IEEE, 2003), http://perso.ens-lyon.fr/patrick.flandrin/publis.html#Communications.

Guyot, S.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).

Huang, N. E.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Huang, Y.

Y. Tian, Y. Huang, and Y. Li, “Image zooming method using 2D EMD technique,” in Proceedings of IEEE 6th World Congress on Intelligent Control and Automation (IEEE, 2006), pp. 10036-10040.

Huntley, J. M.

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59-139.

Kaufmann, G. H.

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

A. Federico and G. H. Kaufmann, “Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes,” Appl. Opt. 45, 1909-1916 (2006).
[CrossRef]

A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44, 2728-2735 (2005).
[CrossRef]

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010-2014 (2003).

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001).

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

P. D. Ruiz and G. H. Kaufmann, “Evaluation of a scale-space filter for speckle noise reduction in electronic speckle pattern interferometry,” Opt. Eng. 37, 2395-2401 (1998).

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

Kim, T.

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182-3193 (2003).

Li, B.

M. Shen, H. Tang, and B. Li, “The modified bidimensional empirical mode decomposition for image denoising,” in Proceedings of IEEE 8th International Conference on Signal Processing (IEEE, 2006), pp. 16-20.

Li, Y.

Y. Tian, Y. Huang, and Y. Li, “Image zooming method using 2D EMD technique,” in Proceedings of IEEE 6th World Congress on Intelligent Control and Automation (IEEE, 2006), pp. 10036-10040.

Linderhed, A.

A. Linderhed, “Variable sampling of the empirical mode decomposition of two-dimensional signals,” Int. J. Wavelets Multires. Inf. Process. 3, 435-452 (2005).

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Long, S. R.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Meignen, S.

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).

Möller, O.

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

Niang, O.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Nunes, J. C.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Pegram, G. G. S.

S. Sinclair and G. G. S. Pegram, “Empirical mode decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting,” Hydrol. Earth Syst. Sciences 9, 127-137 (2005).

Perrier, V.

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).

Rilling, G.

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, Grado, Italy (IEEE, 2003), http://perso.ens-lyon.fr/patrick.flandrin/publis.html#Communications.

Ruiz, P. D.

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

P. D. Ruiz and G. H. Kaufmann, “Evaluation of a scale-space filter for speckle noise reduction in electronic speckle pattern interferometry,” Opt. Eng. 37, 2395-2401 (1998).

Sciammarella, C. A.

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182-3193 (2003).

Shen, M.

M. Shen, H. Tang, and B. Li, “The modified bidimensional empirical mode decomposition for image denoising,” in Proceedings of IEEE 8th International Conference on Signal Processing (IEEE, 2006), pp. 16-20.

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Sinclair, S.

S. Sinclair and G. G. S. Pegram, “Empirical mode decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting,” Hydrol. Earth Syst. Sciences 9, 127-137 (2005).

Tan, S.

Tang, H.

M. Shen, H. Tang, and B. Li, “The modified bidimensional empirical mode decomposition for image denoising,” in Proceedings of IEEE 8th International Conference on Signal Processing (IEEE, 2006), pp. 16-20.

Tian, Y.

Y. Tian, Y. Huang, and Y. Li, “Image zooming method using 2D EMD technique,” in Proceedings of IEEE 6th World Congress on Intelligent Control and Automation (IEEE, 2006), pp. 10036-10040.

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Watkins, L.

Wu, M. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Yang, T. Y.

T. Y. Yang, Finite Element Structural Analysis (Prentice-Hall, 1986), pp. 446-449.

Yen, N. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Appl. Opt. (2)

Hydrol. Earth Syst. Sciences (1)

S. Sinclair and G. G. S. Pegram, “Empirical mode decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting,” Hydrol. Earth Syst. Sciences 9, 127-137 (2005).

IEEE Sig. Proc. Lett. (1)

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Sig. Proc. Lett. 12, 701-704 (2005).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

F. L. Bookstein, “Principal warps: thin-plate splines and the decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567-585 (1989).

Image Vision Comput. (1)

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019-1026 (2003).

Int. J. Wavelets Multires. Inf. Process. (1)

A. Linderhed, “Variable sampling of the empirical mode decomposition of two-dimensional signals,” Int. J. Wavelets Multires. Inf. Process. 3, 435-452 (2005).

Mach. Vision Appl. (1)

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vision Appl. 16, 177-188 (2005).

Opt. Eng. (4)

P. D. Ruiz and G. H. Kaufmann, “Evaluation of a scale-space filter for speckle noise reduction in electronic speckle pattern interferometry,” Opt. Eng. 37, 2395-2401 (1998).

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010-2014 (2003).

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182-3193 (2003).

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001).

Opt. Lasers Eng. (2)

P. D. Ruiz, G. H. Kaufmann, O. Möller, and G. E. Galizzi, “Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements,” Opt. Lasers Eng. 32, 473-484 (2000).

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723-729 (2007).

Opt. Lett. (1)

Proc. R. Soc. London Ser. A. (1)

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A. 454, 903-995 (1998).

Speckle noise reduction in television holography fringes using wavelet thresholding (1)

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

Other (6)

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59-139.

K. Creath, “Temporal phase method,” in Interferogram Analysis, D. Robinson and G. Reid, eds. (Institute of Physics, 1993), pp. 94-140.

Y. Tian, Y. Huang, and Y. Li, “Image zooming method using 2D EMD technique,” in Proceedings of IEEE 6th World Congress on Intelligent Control and Automation (IEEE, 2006), pp. 10036-10040.

T. Y. Yang, Finite Element Structural Analysis (Prentice-Hall, 1986), pp. 446-449.

M. Shen, H. Tang, and B. Li, “The modified bidimensional empirical mode decomposition for image denoising,” in Proceedings of IEEE 8th International Conference on Signal Processing (IEEE, 2006), pp. 16-20.

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, Grado, Italy (IEEE, 2003), http://perso.ens-lyon.fr/patrick.flandrin/publis.html#Communications.

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Figures (5)

Fig. 1
Fig. 1

Computer-generated circular DSPI fringes with 4 fringes and a speckle size of 1 pixel: (a) original fringe pattern, (b) denoised fringe pattern obtained with the BEMD after removing the first 4 IMFs.

Fig. 2
Fig. 2

Computer-generated circular DSPI fringes with 14 fringes and a speckle size of 1 pixel: (a) original fringe pattern, (b) denoised fringe pattern obtained with the BEMD after removing the first IMF.

Fig. 3
Fig. 3

Denoised image obtained with the BEMD from a fringe pattern with 14 fringes and a speckle size of 2 pixels. This result is the worst one listed in Table 1 ( Q = 0.42 ).

Fig. 4
Fig. 4

Comparison between both EMD denoising approaches: (a) 2D method (BEMD, 4 IMFs removed), (b) 1D method (1D EMD, 3 IMFs removed).

Fig. 5
Fig. 5

Denoising of experimental DSPI fringes: (a) original fringe pattern, (b) fringe pattern denoised with the BEMD (1 IMF removed), (c) fringe pattern denoised with the 1D EMD (2 IMFs removed), (d) fringe pattern denoised with a Fourier low-pass filter.

Tables (1)

Tables Icon

Table 1 Smoothing of DSPI Fringes Using the BEMD and 1D EMD Approaches

Equations (3)

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y ( x ) = Σ j = 1 j = n IMF j ( x ) + r n ( x ) .
SD = x = 1 x = X y = 1 y = Y | h i k 1 ( x , y ) h i k ( x , y ) | 2 x = 1 x = X y = 1 y = Y h i k 1 2 ( x , y ) < ε ,
Q = σ E O σ E σ O 2 E ¯ O ¯ ( E ¯ ) 2 + ( O ¯ ) 2 2 σ E σ O σ E 2 + σ O 2 ,

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