Abstract

The impact of multiplicative speckle noise on data acquisition in coherent imaging is studied. This demonstrates the possibility to optimally adjust the level of the speckle noise in order to deliberately exploit, with maximum efficacy, the saturation naturally limiting linear image sensors such as CCD cameras, for instance. This constructive action of speckle noise cooperating with saturation can be interpreted as a novel instance of stochastic resonance or a useful-noise effect.

© 2008 Optical Society of America

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  1. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
    [CrossRef]
  2. F. Chapeau-Blondeau and D. Rousseau, “Noise improvements in stochastic resonance: from signal amplification to optimal detection,” Fluct. Noise Lett. 2, 221-233 (2002).
    [CrossRef]
  3. B. M. Jost and B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21, 287-289 (1996).
    [CrossRef] [PubMed]
  4. F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, and F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15, 2674-2680 (1998).
    [CrossRef]
  5. K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
    [CrossRef] [PubMed]
  6. F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
    [CrossRef] [PubMed]
  7. K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
    [CrossRef] [PubMed]
  8. S. Blanchard, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Constructive action of the speckle noise in a coherent imaging system,” Opt. Lett. 32, 1983-1985 (2007).
    [CrossRef] [PubMed]
  9. D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
    [CrossRef]
  10. F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
    [CrossRef]
  11. J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).
  12. S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory (Prentice Hall, 1998).
  13. J. Ohtsubo and A. Ogiwara, “Effects of clippling threshold on clipped speckle intensity,” Opt. Commun. 65, 73-78 (1988).
    [CrossRef]
  14. A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
    [CrossRef]
  15. R. H. Sperry and K. J. Parker, “Segmentation of speckle images based on level-crossing statistics,” J. Opt. Soc. Am. A 3, 490-498 (1991).
    [CrossRef]
  16. F. Goudail, P. Réfrégier, and G. Delyon, “Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images,” J. Opt. Soc. Am. A 21, 1231-1240 (2004).
    [CrossRef]
  17. F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images (Kluwer, 2004).
  18. P. Réfrégier, J. Fade, and M. Roche, “Estimation precision of the degree of polarization from a single speckle intensity image,” Opt. Lett. 32, 739-741 (2007).
    [CrossRef] [PubMed]

2007

2006

F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
[CrossRef]

2004

2003

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
[CrossRef]

2002

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

F. Chapeau-Blondeau and D. Rousseau, “Noise improvements in stochastic resonance: from signal amplification to optimal detection,” Fluct. Noise Lett. 2, 221-233 (2002).
[CrossRef]

2001

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

1998

1996

1991

R. H. Sperry and K. J. Parker, “Segmentation of speckle images based on level-crossing statistics,” J. Opt. Soc. Am. A 3, 490-498 (1991).
[CrossRef]

1990

A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
[CrossRef]

1988

J. Ohtsubo and A. Ogiwara, “Effects of clippling threshold on clipped speckle intensity,” Opt. Commun. 65, 73-78 (1988).
[CrossRef]

Balle, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

Barland, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

Blanchard, S.

S. Blanchard, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Constructive action of the speckle noise in a coherent imaging system,” Opt. Lett. 32, 1983-1985 (2007).
[CrossRef] [PubMed]

F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
[CrossRef]

Brunel, M.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

Chapeau-Blondeau, F.

S. Blanchard, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Constructive action of the speckle noise in a coherent imaging system,” Opt. Lett. 32, 1983-1985 (2007).
[CrossRef] [PubMed]

F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
[CrossRef]

D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
[CrossRef]

F. Chapeau-Blondeau and D. Rousseau, “Noise improvements in stochastic resonance: from signal amplification to optimal detection,” Fluct. Noise Lett. 2, 221-233 (2002).
[CrossRef]

F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, and F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15, 2674-2680 (1998).
[CrossRef]

Delyon, G.

Fade, J.

Gammaitoni, L.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
[CrossRef]

Gazengel, J.

Gindre, D.

Giudici, M.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

Godivier, X.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

Goudail, F.

Hänggi, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
[CrossRef]

Jost, B. M.

Jung, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
[CrossRef]

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory (Prentice Hall, 1998).

Le Floch, A.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

Marchesoni, F.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
[CrossRef]

Marino, F.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

Ogiwara, A.

A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
[CrossRef]

J. Ohtsubo and A. Ogiwara, “Effects of clippling threshold on clipped speckle intensity,” Opt. Commun. 65, 73-78 (1988).
[CrossRef]

Ohtsubo, J.

A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
[CrossRef]

J. Ohtsubo and A. Ogiwara, “Effects of clippling threshold on clipped speckle intensity,” Opt. Commun. 65, 73-78 (1988).
[CrossRef]

Parker, K. J.

R. H. Sperry and K. J. Parker, “Segmentation of speckle images based on level-crossing statistics,” J. Opt. Soc. Am. A 3, 490-498 (1991).
[CrossRef]

Réfrégier, P.

Rivoire, G.

Roche, M.

Rojas Varela, J.

D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
[CrossRef]

Ropars, G.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

Rousseau, D.

S. Blanchard, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Constructive action of the speckle noise in a coherent imaging system,” Opt. Lett. 32, 1983-1985 (2007).
[CrossRef] [PubMed]

F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
[CrossRef]

D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
[CrossRef]

F. Chapeau-Blondeau and D. Rousseau, “Noise improvements in stochastic resonance: from signal amplification to optimal detection,” Fluct. Noise Lett. 2, 221-233 (2002).
[CrossRef]

Sakai, H.

A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
[CrossRef]

Saleh, B. E. A.

Singh, K. P.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

Sperry, R. H.

R. H. Sperry and K. J. Parker, “Segmentation of speckle images based on level-crossing statistics,” J. Opt. Soc. Am. A 3, 490-498 (1991).
[CrossRef]

Vaudelle, F.

Fluct. Noise Lett.

F. Chapeau-Blondeau and D. Rousseau, “Noise improvements in stochastic resonance: from signal amplification to optimal detection,” Fluct. Noise Lett. 2, 221-233 (2002).
[CrossRef]

J. Opt. Soc. Am. A

R. H. Sperry and K. J. Parker, “Segmentation of speckle images based on level-crossing statistics,” J. Opt. Soc. Am. A 3, 490-498 (1991).
[CrossRef]

F. Goudail, P. Réfrégier, and G. Delyon, “Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images,” J. Opt. Soc. Am. A 21, 1231-1240 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. Ohtsubo and A. Ogiwara, “Effects of clippling threshold on clipped speckle intensity,” Opt. Commun. 65, 73-78 (1988).
[CrossRef]

A. Ogiwara, H. Sakai, and J. Ohtsubo, “Real-time optical joint transform correlator for velocity measurement using clipped speckle intensity,” Opt. Commun. 78, 322-326 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev. E

D. Rousseau, J. Rojas Varela, and F. Chapeau-Blondeau, “Stochastic resonance for nonlinear sensors with saturation,” Phys. Rev. E 67, 021102 (2003).
[CrossRef]

F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, “Noise-enhanced Fisher information in parallel arrays of sensors with saturation,” Phys. Rev. E 74, 031102 (2006).
[CrossRef]

Phys. Rev. Lett.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef] [PubMed]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef] [PubMed]

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Lever-assisted two-noise stochastic resonance,” Phys. Rev. Lett. 90, 073901 (2003).
[CrossRef] [PubMed]

Rev. Mod. Phys.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223-287 (1998).
[CrossRef]

Other

F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images (Kluwer, 2004).

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory (Prentice Hall, 1998).

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Figures (3)

Fig. 1
Fig. 1

Normalized cross covariance C S Y (A) and rms error Q S Y (B) as a function of the rms amplitude 2 σ of the exponential speckle noise when θ = 1 , p 1 = 0.27 , and I 0 = 0.5 at various I 1 . The solid curve stands for the theoretical expressions of Eqs. (3, 4). The discrete data sets (circles) are obtained by injecting into Eq. (1) real speckle images collected from the experimental setup of [8].

Fig. 2
Fig. 2

(Left) Input image S ( u , v ) , with size 1024 × 1024 pixels, used for the experimental validation presented in Fig. 1, where the object is occupying p 1 = 27 % of the image surface and parameters I 0 = 0.5 , I 1 = 1.5 . (Right) Corresponding intermediate image X ( u , v ) obtained with a speckle noise rms amplitude 2 σ = 0.42 .

Fig. 3
Fig. 3

(Left) Histogram of background ( ) and object ( * ) regions in intermediate image X ( u , v ) of Eq. (1) on a logarithmic scale. Input image S ( u , v ) is the same as in Fig. 2 (left). The solid curves are the theoretical histograms calculated from the exponential model of Eq. (14). The dashed curve stands for the saturating level θ = 1 of the acquisition image device. Speckle noise is obtained from the experimental setup of [8] with an rms amplitude 2 σ = 0.42 , corresponding to the optimal value of normalized cross covariance C S Y . (Right) Binary image representing only the pixel saturated in the acquired image Y ( u , v ) under the acquisition conditions of the left panel of this figure.

Equations (24)

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S ( u , v ) × N ( u , v ) = X ( u , v ) ,
Y ( u , v ) = g [ X ( u , v ) ] .
C S Y = S Y S Y S 2 S 2 Y 2 Y 2 ,
Q S Y = ( S Y ) 2 .
g ( x ) = { 0 for x 0 x for 0 < x < θ θ for x θ .
Pr { Y [ y , y + d y [ S = s } = Pr { N [ y s , y s + d y s [ } = p N ( y s ) d y s ,
Pr { Y = θ S = s } = Pr { s N θ } = Pr { N θ s } = 1 F N ( θ s ) ,
Y = s y = 0 θ y p N ( y s ) d y s p S ( s ) d s + s θ [ 1 F N ( θ s ) ] p S ( s ) d s .
Y = θ + s [ s G N ( θ s ) θ F N ( θ s ) ] p S ( s ) d s .
S Y = s y = 0 θ s y p N ( y s ) d y s p S ( s ) d s + s s θ [ 1 F N ( θ s ) ] p S ( s ) d s ,
S Y = θ S + s [ s 2 G N ( θ s ) θ s F N ( θ s ) ] p S ( s ) d s .
Y 2 = s y = 0 θ y 2 p N ( y s ) d y s p S ( s ) d s + s θ 2 [ 1 F N ( θ s ) ] p S ( s ) d s .
Y 2 = θ 2 + s [ s 2 H N ( θ s ) θ 2 F N ( θ s ) ] p S ( s ) d s .
p N ( n ) = 1 σ exp ( n σ ) , n 0 ,
F N ( n ) = 1 exp ( n σ ) , n 0 ,
G N ( n ) = 0 n n p N ( n ) d n = σ [ 1 ( n σ + 1 ) exp ( n σ ) ] , n 0 ,
H N ( n ) = 0 n n 2 p N ( n ) d n = σ 2 { 2 [ ( n σ ) 2 + 2 n σ + 2 ] exp ( n σ ) } , n 0 .
Y = σ S σ s s exp ( θ s σ ) p S ( s ) d s ,
S Y = σ S 2 σ s s 2 exp ( θ s σ ) p S ( s ) d s ,
Y 2 = 2 σ 2 S 2 2 σ s ( σ s 2 + θ s ) exp ( θ s σ ) p S ( s ) d s .
p S ( s ) = p 1 δ ( s I 1 ) + ( 1 p 1 ) δ ( s I 0 ) ,
Y = σ S σ [ p 1 I 1 exp ( θ I 1 σ ) + ( 1 p 1 ) I 0 exp ( θ I 0 σ ) ] ,
S Y = σ S 2 σ [ p 1 I 1 2 exp ( θ I 1 σ ) + ( 1 p 1 ) I 0 2 exp ( θ I 0 σ ) ] ,
Y 2 = 2 σ 2 S 2 2 σ [ p 1 ( σ I 1 2 + θ I 1 ) exp ( θ I 1 σ ) + ( 1 p 1 ) ( σ I 0 2 + θ I 0 ) exp ( θ I 0 σ ) ] .

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