Abstract

Digital speckle pattern interferometry (DSPI) fringes contain low spatial information degraded with speckle noise and background intensity. The denoising technique proposed recently based on bi-dimensional empirical mode decomposition (BEMD) could implement noise reduction adaptively. However, the major drawback of BEMD, called mode mixing, has affected its practical application. With noise-assisted data analysis (NADA) method, bi-dimensional ensemble empirical mode decomposition (BEEMD) was proposed, which has solved the problem of mode mixing. The denoising approach based on BEEMD will be presented, compared with other classic denoising methods and evaluated both qualitatively and quantitatively using computer-simulated and experimental DSPI fringes.

© 2011 OSA

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References

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  1. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47(14), 2592–2598 (2008).
    [CrossRef] [PubMed]
  2. Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal. 1(01), 1–41 (2009).
    [CrossRef]
  3. Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
    [CrossRef]
  4. 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(9), 1909–1916 (2006).
    [CrossRef] [PubMed]
  5. R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
    [CrossRef]
  6. A. Federico 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]
  7. X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34(13), 2033–2035 (2009).
    [CrossRef] [PubMed]
  8. A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44(14), 2728–2735 (2005).
    [CrossRef] [PubMed]
  9. 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(8), 2395 (1998).
    [CrossRef]
  10. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
    [CrossRef]
  11. A. W. Leissa, “The free vibration of rectangular plates,” J. Sound Vibrat. 31(3), 257–293 (1973).
    [CrossRef]
  12. C. Loizou, C. Christodoulou, C. S. Pattichis, R. Istepanian, M. Pantziaris, and A. Nicolaides, “Speckle reduction in ultrasound images of atherosclerotic carotid plaque,” Proc. IEEE 14th Intl. Conf. Digital Signal Process, 525–528 (2002).
  13. T. R. Crimmins, “Geometric filter for speckle reduction,” Appl. Opt. 24(10), 1438–1443 (1985).
    [CrossRef] [PubMed]
  14. C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
    [CrossRef]
  15. R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
    [CrossRef]
  16. R. Kumar, “Wavelet filtering applied to time-average digital speckle pattern interferometry fringes,” Opt. Laser Technol. 33(8), 567–571 (2001).
    [CrossRef]
  17. K. Creath, “Temporal phase method,” in Interferogram Analysis, D. Robinson, and G. Reid, eds. (Institute of Physics, 1993), pp. 94–140.
  18. Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
    [CrossRef]

2011 (1)

R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
[CrossRef]

2009 (4)

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal. 1(01), 1–41 (2009).
[CrossRef]

Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
[CrossRef]

X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34(13), 2033–2035 (2009).
[CrossRef] [PubMed]

Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
[CrossRef]

2008 (1)

2006 (1)

2005 (1)

2004 (1)

R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
[CrossRef]

2002 (2)

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[CrossRef]

2001 (2)

A. Federico 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]

R. Kumar, “Wavelet filtering applied to time-average digital speckle pattern interferometry fringes,” Opt. Laser Technol. 33(8), 567–571 (2001).
[CrossRef]

1998 (1)

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(8), 2395 (1998).
[CrossRef]

1985 (1)

1973 (1)

A. W. Leissa, “The free vibration of rectangular plates,” J. Sound Vibrat. 31(3), 257–293 (1973).
[CrossRef]

Bernini, M. B.

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[CrossRef]

Chen, X.

Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
[CrossRef]

Crimmins, T. R.

Federico, A.

He, Z.

Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
[CrossRef]

Huang, N. E.

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal. 1(01), 1–41 (2009).
[CrossRef]

Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
[CrossRef]

Jena, D. P.

R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
[CrossRef]

Jiang, T.

Kaufmann, G. H.

Kazmi, S. A.

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

Kumar, R.

R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
[CrossRef]

R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
[CrossRef]

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

R. Kumar, “Wavelet filtering applied to time-average digital speckle pattern interferometry fringes,” Opt. Laser Technol. 33(8), 567–571 (2001).
[CrossRef]

Lei, Y.

Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
[CrossRef]

Leissa, A. W.

A. W. Leissa, “The free vibration of rectangular plates,” J. Sound Vibrat. 31(3), 257–293 (1973).
[CrossRef]

Ruiz, P. D.

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(8), 2395 (1998).
[CrossRef]

Shakher, C.

R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
[CrossRef]

R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
[CrossRef]

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

Singh, I. P.

R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
[CrossRef]

Singh, S. K.

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[CrossRef]

Wu, Z.

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal. 1(01), 1–41 (2009).
[CrossRef]

Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
[CrossRef]

Zhao, H.

Zhou, X.

Zi, Y.

Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
[CrossRef]

Adv. Adapt. Data Anal. (2)

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal. 1(01), 1–41 (2009).
[CrossRef]

Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition,” Adv. Adapt. Data Anal. 1(03), 339–372 (2009).
[CrossRef]

Appl. Opt. (4)

IEEE Signal Process. Lett. (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[CrossRef]

J. Sound Vibrat. (1)

A. W. Leissa, “The free vibration of rectangular plates,” J. Sound Vibrat. 31(3), 257–293 (1973).
[CrossRef]

Mech. Syst. Signal Process. (1)

Y. Lei, Z. He, and Y. Zi, “Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 23(4), 1327–1338 (2009).
[CrossRef]

Opt. Eng. (3)

C. Shakher, R. Kumar, S. K. Singh, and S. A. Kazmi, “Application of wavelet filtering for vibration analysis using digital speckle pattern interferometry,” Opt. Eng. 41(1), 176 (2002).
[CrossRef]

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(8), 2395 (1998).
[CrossRef]

A. Federico 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]

Opt. Laser Technol. (1)

R. Kumar, “Wavelet filtering applied to time-average digital speckle pattern interferometry fringes,” Opt. Laser Technol. 33(8), 567–571 (2001).
[CrossRef]

Opt. Lasers Eng. (1)

R. Kumar, I. P. Singh, and C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41(1), 81–93 (2004).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

R. Kumar, D. P. Jena, and C. Shakher, “Application of wavelet transform and image morphology in processing vibration speckle interferogram for automatic analysis,” Proc. SPIE 8082, 80821Y, 80821Y-5 (2011).
[CrossRef]

Other (2)

C. Loizou, C. Christodoulou, C. S. Pattichis, R. Istepanian, M. Pantziaris, and A. Nicolaides, “Speckle reduction in ultrasound images of atherosclerotic carotid plaque,” Proc. IEEE 14th Intl. Conf. Digital Signal Process, 525–528 (2002).

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

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Figures (7)

Fig. 1
Fig. 1

Decomposition of Lena using BEMD. (a) Original Lena image. (b)–(e) 1–4 orders of 2D IMF components, from fine to large scale.

Fig. 2
Fig. 2

Decomposition of Lena using BEEMD. (a) Original Lena image. (b)–(e) 1–4 orders 2D IMF components, from fine to large scale.

Fig. 3
Fig. 3

(a) Variation of X(K). (b) Variation of Y(K).

Fig. 4
Fig. 4

Computer simulated DSPI fringes with a speckle size of 1 pixel. (a) Original DSPI fringe. (b) Filtered DSPI fringe using BEEMD. (c) Filtered DSPI fringe using BEMD.

Fig. 5
Fig. 5

Component separation of Fig. 4(a) using BEEMD-based denoising method. (a) First component corresponding to speckle noise. (b) Middle component corresponding to desirable fundamental component. (c) Last component corresponding to background intensity.

Fig. 6
Fig. 6

Unfiltered experimental DSPI fringes for a cantilever beam.

Fig. 7
Fig. 7

Filtered DSPI fringes. (a) Low-pass filtering based on Fourier transforms. (b) Average followed by Daubechies wavelet. (c) Average followed by Symlet wavelet. (d) Denoising based on EEMD. (e) Denoising based on BEMD. (f) Denoising based on BEEMD.

Tables (2)

Tables Icon

Table 1 . Quality Index of DSPI Fringe Using BEEMD and BEMD Approaches

Tables Icon

Table 2 Speckle Index and SNR Using Six Denoising Methods

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ) = I O ( x , y ) + I R ( x , y ) + 2 I O ( x , y ) I R ( x , y ) cos ( ϕ ( x , y ) + Δ ϕ ( x , y ) ) ,
I ( x , y ) = a ( x , y ) + b ( x , y ) cos ϕ ( x , y ) + n ( x , y ) ,
I ( x , y ) = j = 1 K c ¯ j ( x , y ) + j = K + 1 N c ¯ j ( x , y ) + r ¯ ( x , y ) ,
X ( K ) = [ R c ( x , y ) ] 2 d x d y [ R n ( x , y ) ] 2 d x d y ,
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 ,
D 4 ω + ρ 2 ω t 2 = 0 ,
C = var ( x ¯ ) E ( x ¯ ) = σ m ,
S N R = 1 C .

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