Abstract

Filtering off noise from a fringe pattern is one of the key tasks in optical interferometry. In this Letter, using some suitable function spaces to model different components of a fringe pattern, we propose a new fringe pattern denoising method based on image decomposition. In our method, a fringe image is divided into three parts: low-frequency fringe, high-frequency fringe, and noise, which are processed in different spaces. An adaptive threshold in wavelet shrinkage involved in this algorithm improves its denoising performance. Simulation and experimental results show that our algorithm obtains smooth and clean fringes with different frequencies while preserving fringe features effectively.

© 2012 Optical Society of America

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References

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  1. D. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).
  2. Q. Kemao, L. Nam, L. Feng, and S. Soon, Appl. Opt. 46, 7412 (2007).
    [CrossRef]
  3. J. Villa, J. Quiroga, and I. De la Rosa, Opt. Lett. 34, 1741 (2009).
    [CrossRef]
  4. J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
    [CrossRef]
  5. C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, Opt. Lett. 33, 2179 (2008).
    [CrossRef]
  6. C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, Opt. Express 17, 5606 (2009).
    [CrossRef]
  7. H. Wang and Q. Kemao, Appl. Opt. 50, 1687 (2011).
    [CrossRef]
  8. Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, 2001).
  9. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd. ed. (Springer-Verlag, 2006).
  10. L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
    [CrossRef]
  11. J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
    [CrossRef]
  12. K. K. Gupta and R. Gupta, in Proceedings of International Conference on Signal Processing, Communications and Networking, 2007 (IEEE, 2007), pp. 81–85.
  13. C. Tang, T. Gao, S. Yan, L. Wang, and J. Wu, Opt. Express 18, 8942 (2010).
    [CrossRef]

2011

2010

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

C. Tang, T. Gao, S. Yan, L. Wang, and J. Wu, Opt. Express 18, 8942 (2010).
[CrossRef]

2009

2008

2007

2005

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

1992

L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Antonio Quiroga, J.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

Aubert, G.

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd. ed. (Springer-Verlag, 2006).

Aujol, J.

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Chambolle, A.

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Chang, Y.

Cui, X.

De la Rosa, I.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

J. Villa, J. Quiroga, and I. De la Rosa, Opt. Lett. 34, 1741 (2009).
[CrossRef]

Fatemi, E.

L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Feng, L.

Gao, T.

González, E.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

Gupta, K. K.

K. K. Gupta and R. Gupta, in Proceedings of International Conference on Signal Processing, Communications and Networking, 2007 (IEEE, 2007), pp. 81–85.

Gupta, R.

K. K. Gupta and R. Gupta, in Proceedings of International Conference on Signal Processing, Communications and Networking, 2007 (IEEE, 2007), pp. 81–85.

Han, L.

Kemao, Q.

Kornprobst, P.

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd. ed. (Springer-Verlag, 2006).

Meyer, Y.

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, 2001).

Nam, L.

Osher, S.

L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Quiroga, J.

Reid, G.

D. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).

Ren, H.

Robinson, D.

D. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).

Rodríguez-Vera, R.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

Rudin, L.

L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Soon, S.

Tang, C.

Tang, K.

Villa, J.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

J. Villa, J. Quiroga, and I. De la Rosa, Opt. Lett. 34, 1741 (2009).
[CrossRef]

Wang, H.

Wang, L.

Wang, X.

Wang, Z.

Wu, J.

Yan, S.

Zhou, D.

Appl. Opt.

Int. J. Comput. Vis.

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

J. Villa, R. Rodríguez-Vera, J. Antonio Quiroga, I. De la Rosa, and E. González, Opt. Lasers Eng. 48, 650 (2010).
[CrossRef]

Opt. Lett.

Physica D

L. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Other

K. K. Gupta and R. Gupta, in Proceedings of International Conference on Signal Processing, Communications and Networking, 2007 (IEEE, 2007), pp. 81–85.

D. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, 1993).

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, 2001).

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd. ed. (Springer-Verlag, 2006).

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Figures (3)

Fig. 1.
Fig. 1.

Denoising a simulated fringe pattern (from top left to bottom right): noisy image, u, v, w, u+v of the proposed method, and the result by TV method.

Fig. 2.
Fig. 2.

Denoising a simulated fringe pattern (from left to right): noisy image, u, and w of proposed method.

Fig. 3.
Fig. 3.

Denoising an experimental fringe pattern (from top left to bottom right): noisy image, u, v, w, u+v of the proposed method, and the result by TV method.

Equations (11)

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

f(x)=a(x)+b(x)cos[ϕ(x)]+η(x),
inf(u,v)BV(Ω)×L2(Ω)f=u+vΩ|u|dx+1λvL22,
inf(u,v)BV(Ω)×G(Ω)f=u+vΩ|u|dx+αvG,
inf(u,v,w)H1(Ω)×G(Ω)×E(Ω)f=u+v+wΩ|u|2dx+αvG+βwE,
infwE(Ω),wEδfuvwL22.
infvG(Ω),vGμfuvwL22.
infuH1(Ω)Ω|u|2dx+1λfuvwL22.
u0=v0=w0=0.
wn+1=funvnWST(funvn,δ),
vn+1=PGμ(funwn),
un+1=F1{11+λ(2π|ξ|)2F(fvnwn)},

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