Abstract

We present an effective method for speckle noise removal in digital speckle pattern interferometry, which is based on a wave-atom thresholding technique. Wave atoms are a variant of 2D wavelet packets with a parabolic scaling relation and improve the sparse representation of fringe patterns when compared with traditional expansions. The performance of the denoising method is analyzed by using computer-simulated fringes, and the results are compared with those produced by wavelet and curvelet thresholding techniques. An application of the proposed method to reduce speckle noise in experimental data is also presented.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2006 (1)

2005 (1)

2004 (1)

E. J. Candès and D. L. Donoho, Commun. Pure Appl. Math. 57, 219 (2004).
[CrossRef]

2003 (4)

G. H. Kaufmann, Opt. Eng. 42, 2010 (2003).
[CrossRef]

C. A. Sciammarella and T. Kim, Opt. Eng. 42, 3182 (2003).
[CrossRef]

A. Federico and G. H. Kaufmann, Appl. Opt. 42, 7066 (2003).
[CrossRef] [PubMed]

N. K. Mohan and P. K. Rastogi, Opt. Lasers Eng. 40, 439 (2003).
[CrossRef]

2002 (1)

A. Federico and G. H. Kaufmann, Opt. Eng. 41, 3209 (2002).
[CrossRef]

2001 (1)

A. Federico and G. H. Kaufmann, Opt. Eng. 40, 2598 (2001).
[CrossRef]

1999 (1)

Barnes, T.

Bovik, A. C.

A. C. Bovik, Handbook of Image and Video Processing (Academic, 2005).

Candès, E. J.

E. J. Candès and D. L. Donoho, Commun. Pure Appl. Math. 57, 219 (2004).
[CrossRef]

Demanet, L.

L. Demanet, "Curvelets, wave atoms, and wave equations," Ph.D. Thesis, Caltech (2006), http://math.stanford.edu/~laurent/papers/ThesisDemanet.pdf.

Donoho, D. L.

E. J. Candès and D. L. Donoho, Commun. Pure Appl. Math. 57, 219 (2004).
[CrossRef]

Federico, A.

Kaufmann, G. H.

Kim, T.

C. A. Sciammarella and T. Kim, Opt. Eng. 42, 3182 (2003).
[CrossRef]

Mohan, N. K.

N. K. Mohan and P. K. Rastogi, Opt. Lasers Eng. 40, 439 (2003).
[CrossRef]

Rastogi, P. K.

N. K. Mohan and P. K. Rastogi, Opt. Lasers Eng. 40, 439 (2003).
[CrossRef]

Sciammarella, C. A.

C. A. Sciammarella and T. Kim, Opt. Eng. 42, 3182 (2003).
[CrossRef]

Tan, S.

Watkins, L.

Appl. Opt. (3)

Commun. Pure Appl. Math. (1)

E. J. Candès and D. L. Donoho, Commun. Pure Appl. Math. 57, 219 (2004).
[CrossRef]

Opt. Eng. (4)

A. Federico and G. H. Kaufmann, Opt. Eng. 41, 3209 (2002).
[CrossRef]

A. Federico and G. H. Kaufmann, Opt. Eng. 40, 2598 (2001).
[CrossRef]

C. A. Sciammarella and T. Kim, Opt. Eng. 42, 3182 (2003).
[CrossRef]

G. H. Kaufmann, Opt. Eng. 42, 2010 (2003).
[CrossRef]

Opt. Lasers Eng. (1)

N. K. Mohan and P. K. Rastogi, Opt. Lasers Eng. 40, 439 (2003).
[CrossRef]

Opt. Lett. (1)

Other (4)

L. Demanet, "Curvelets, wave atoms, and wave equations," Ph.D. Thesis, Caltech (2006), http://math.stanford.edu/~laurent/papers/ThesisDemanet.pdf.

http://math.stanford.edu/~laurent/html/software.html.

A. C. Bovik, Handbook of Image and Video Processing (Academic, 2005).

http://www.curvelet.org/software.html.

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Figures (4)

Fig. 1
Fig. 1

Computer-simulated DSPI fringe pattern.

Fig. 2
Fig. 2

Filtered image of Fig. 1 using WA thresholding.

Fig. 3
Fig. 3

Experimental DSPI fringe pattern.

Fig. 4
Fig. 4

Filtered image of Fig. 3 using WA thresholding.

Tables (1)

Tables Icon

Table 1 Quality Index Q Obtained for Wavelet, Curvelet, and WA Thresholding as a Function of the Ratio α

Equations (7)

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

ϕ ̂ μ C M 2 j ( 1 + 2 j ω ω μ ) M + C M 2 j ( 1 + 2 j ω + ω μ ) M
x μ = ( x 1 , x 2 ) μ = 2 j ( n 1 , n 2 ) ,
ω μ = ( ω 1 , ω 2 ) μ = π 2 j ( m 1 , m 2 ) ,
ψ ̂ m 1 0 ( ω 1 ) = e i ω 1 2 { e i α m 1 g [ ϵ m 1 ( ω 1 π m 1 π 2 ) ] + e i α m 1 g [ ϵ m 1 + 1 ( ω 1 + π m 1 + π 2 ) ] } ,
ϕ μ + ( x 1 , x 2 ) = ψ m 1 j ( x 1 2 j n 1 ) ψ m 2 j ( x 2 2 j n 2 ) ,
ϕ μ ( x 1 , x 2 ) = H ψ m 1 j ( x 1 2 j n 1 ) H ψ m 2 j ( x 2 2 j n 2 ) ,
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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