Abstract

In imaging, the choice of an observation scale is conventionally settled by the operator in charge of the image acquisition, who is left alone with tuning the framing and zooming parameters of the imaging system. In a somewhat decoupled manner, the operator in charge of processing the data has access to the images after their acquisition, and seeks to extract information from the observed scene. This Letter proposes a manifestation of the interest of an alternative joint acquisition-processing approach. We demonstrate with quantitative informational measures how the choice of an observation scale can be directly related to the performance of the final information processing task. Illustrations are given with various tools from statistical information theory with possible applications of practical interest to any noisy imaging domains.

© 2011 Optical Society of America

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References

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  1. P. Réfrégier, Noise Theory and Application to Physics (Springer, 2004).
  2. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
    [CrossRef]
  3. J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).
  4. F. Chapeau-Blondeau and D. Rousseau, Physica A 388, 3969 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. F. Galland and P. Réfrégier, Opt. Lett. 32, 2514 (2007).
    [CrossRef] [PubMed]
  7. Y. Xu, Y. Zhao, C. Jin, Z. Qu, L. Liu, and X. Sun, Opt. Lett. 35, 475 (2010).
    [CrossRef] [PubMed]
  8. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, Opt. Lett. 33, 974 (2008).
    [CrossRef] [PubMed]

2010 (1)

2009 (1)

F. Chapeau-Blondeau and D. Rousseau, Physica A 388, 3969 (2009).
[CrossRef]

2008 (1)

2007 (1)

1994 (1)

Baraniuk, R. G.

Beléndez, A.

Carretero, L.

Chan, W. L.

Chapeau-Blondeau, F.

F. Chapeau-Blondeau and D. Rousseau, Physica A 388, 3969 (2009).
[CrossRef]

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
[CrossRef]

Fimia, A.

Galland, F.

Jin, C.

Liu, L.

Mittleman, D. M.

Moravec, M. L.

Qu, Z.

Réfrégier, P.

F. Galland and P. Réfrégier, Opt. Lett. 32, 2514 (2007).
[CrossRef] [PubMed]

P. Réfrégier, Noise Theory and Application to Physics (Springer, 2004).

Rissanen, J.

J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).

Rousseau, D.

F. Chapeau-Blondeau and D. Rousseau, Physica A 388, 3969 (2009).
[CrossRef]

Sun, X.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
[CrossRef]

Xu, Y.

Zhao, Y.

Opt. Lett. (4)

Physica A (1)

F. Chapeau-Blondeau and D. Rousseau, Physica A 388, 3969 (2009).
[CrossRef]

Other (3)

P. Réfrégier, Noise Theory and Application to Physics (Springer, 2004).

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
[CrossRef]

J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).

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Figures (1)

Fig. 1
Fig. 1

Optimal number of bins K 0 * and K 1 * , giving the minimum description length associated with the empirical histograms of background L ( Y 0 ) and object L ( Y 1 ) of Eq. (6) as a function of the observation scale p 1 = N 1 / N of the object. An optimal scale p 1 * is at K 1 * = K 0 * . Object is distributed following a centered Gaussian probability density with standard deviation σ 1 = 1 and N = 1024 . Various backgrounds, identical to the object (circles), distributed following a centered Laplacian (stars), or exponential (diamonds) probability densities [1], with σ 0 = 1 in all cases. Corresponding optimal observation scales are located around p 1 * = 0.5 (circles), p 1 * = 0.7 (stars), p 1 * = 0.6 (diamonds).

Equations (6)

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p 1 * = a p 00 1 a ( p 00 + p 11 1 ) ,
a = 1 + exp [ ln ( 2 ) i = 0 i = 1 ( 1 ) i ( h ( p i i ) + h ( 1 p i i ) ) p 00 + p 11 1 ] .
J Y ( I i ) = + 1 p ( y | s = I i ) [ I i p ( y | s = I i ) ] 2 d y ,
var min = arg min { N 1 } 1 N 1 J Y ( I 1 ) + 1 ( N N 1 ) J Y ( I 0 ) ,
p 1 * = 1 1 + J Y ( I 1 ) J Y ( I 0 ) .
L ( Y i ) = log [ A N i , K i ] + N i [ H ( f ^ k i ) log ( K i ) ] ,

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