Abstract

We present a 3D imaging method to reduce speckle noise that exists in coherent imaging systems. This approach is based on integral imaging (II). The elemental images set having speckle-noise patterns of a 3D object is obtained by II technique under coherent illumination. The computational geometrical ray-propagation algorithm is applied to the elemental images in order to reconstruct the original 3D object. A uniform probability-density function is assumed for modeling the phase distribution of the speckle patterns. The statistical point estimator is used for 3D speckle removal. Speckle index is calculated to compare the computational reconstruction using the proposed method with that of conventional coherent image degraded by speckle patterns for 3D object reconstruction and by object recognition. Experimental results are presented. The speckle index, mean square error, and signal-to-noise ratio are used as performance metrics and are shown to have been significantly improved by the proposed method to reduce speckle noise in the 3D object reconstruction. 3D reconstruction experiments of objects with reduced speckle noise are presented. To the best of our knowledge, this is the first report on 3D speckle removal using II and statistical estimation algorithms.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).
  10. R. Gonzalez, R. Woods, and S. Eddins, Digital Image Processing (Prentice Hall, 2003).

2008 (1)

2007 (1)

2006 (1)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

2004 (1)

1980 (1)

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

1908 (1)

G. Lippmann, Compt. Rend. 146, 446 (1908).

Benton, S.

S. Benton, Selected Papers on Three-dimensional Displays (SPIE, 2001).

Bertaux, N.

Castro, A.

Eddins, S.

R. Gonzalez, R. Woods, and S. Eddins, Digital Image Processing (Prentice Hall, 2003).

Frauel, Y.

Gonzalez, R.

R. Gonzalez, R. Woods, and S. Eddins, Digital Image Processing (Prentice Hall, 2003).

Goodman, J.

J. Goodman, Speckle Phenomena: Theory and Applications (Roberts & Company, 2006).

Hennelly, B. M.

Javidi, B.

Lippmann, G.

G. Lippmann, Compt. Rend. 146, 446 (1908).

Matoba, O.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Maycock, J.

McDonald, J. B.

Mukhopadhyay, N.

N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Naughton, T. J.

Okoshi, T.

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

Réfrégier, P.

Tahajuerce, E.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Tavakoli, B.

Watson, E.

Woods, R.

R. Gonzalez, R. Woods, and S. Eddins, Digital Image Processing (Prentice Hall, 2003).

Compt. Rend. (1)

G. Lippmann, Compt. Rend. 146, 446 (1908).

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Proc. IEEE (2)

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Other (4)

J. Goodman, Speckle Phenomena: Theory and Applications (Roberts & Company, 2006).

N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).

R. Gonzalez, R. Woods, and S. Eddins, Digital Image Processing (Prentice Hall, 2003).

S. Benton, Selected Papers on Three-dimensional Displays (SPIE, 2001).

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Figures (5)

Fig. 1
Fig. 1

Coherent II for 3D speckle-noise removal.

Fig. 2
Fig. 2

Elemental images with speckle noise: (a) car I and (b) car II.

Fig. 3
Fig. 3

Slices of 3D reconstructed integral images using the proposed method show substantially reduced speckle compared with Fig. 2: (a) car I and (b) car II.

Fig. 4
Fig. 4

Nontraining true-class object car I: (a) sample of a noisy elemental image and (b) speckle-reduced image.

Fig. 5
Fig. 5

(a) SNR and (b) MSE plots for true- and false-class objects in Fig. 2 reconstructed by II (see Fig 3).

Equations (7)

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I s p = I o p + [ n s p ( Φ ) × I o p ] ,
I s p ( i ) = I o p ( i ) + [ n s p ( Φ ( i ) ) × I o p ( i ) ] for i = 1 , , N x × N y .
M = 1 N x × N y i = 1 N x × N y I s p ( i ) .
II p = I o p + E [ n s p ( Φ ) × I o p ] ,
SNR = x = 1 n x y = 1 n y II ref ( x , y ; z = z 0 ) 2 x = 1 n x y = 1 n y [ II ref ( x , y ; z = z 0 ) II inp ( x , y ; z = z 0 ) ] 2 ,
MSE = x = 1 n x y = 1 n y [ II ref ( x , y ; z = z 0 ) II inp ( x , y ; z = z 0 ) ] 2 n x × n y .
R = false-class MSE true-class MSE .

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