Abstract

We analyze the performance of a nonlinear correlation called the Locally Adaptive Contrast Invariant Filter in the presence of spatially disjoint noise under the peak-to-sidelobe ratio (PSR) metric. We show that the PSR using the nonlinear correlation improves as the disjoint noise intensity increases, whereas, for common linear filtering, it goes to zero. Experimental results as well as comparisons with a classical matched filter are given.

© 2010 Optical Society of America

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References

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2005 (1)

2004 (1)

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[CrossRef]

2003 (1)

2002 (1)

1996 (1)

1995 (1)

1994 (1)

1993 (2)

1992 (1)

1990 (1)

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inform. Theory 10, 139–145 (1964).
[CrossRef]

Arsenault, H. H.

Ferreira, C.

García-Martínez, P.

Goudail, F.

Hassebrook, L.

Javidi, B.

Laude, V.

Lefebvre, D.

Refregier, Ph.

Roy, S.

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[CrossRef]

D. Lefebvre, H. H. Arsenault, and S. Roy, “Nonlinear filter for pattern recognition invariant to illumination and to out-of-plane rotations,” Appl. Opt. 42, 4658–4662 (2003).
[CrossRef] [PubMed]

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inform. Theory 10, 139–145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

Wang, J.

Willet, P.

Zhang, G.

Appl. Opt. (6)

IEEE Trans. Inform. Theory (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inform. Theory 10, 139–145 (1964).
[CrossRef]

Opt. Commun. (1)

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[CrossRef]

Opt. Lett. (4)

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Figures (6)

Fig. 1
Fig. 1

Original scene.

Fig. 2
Fig. 2

Scene that contains the target to detect is corrupted by disjoint noise (the standard deviation of noise is simulated by MATLAB with σ = 300 ).

Fig. 3
Fig. 3

Matched filter’s PSR versus the standard deviation of the disjoint noise.

Fig. 4
Fig. 4

LACIF’s PSR versus the standard deviation of the disjoint noise.

Fig. 5
Fig. 5

Local variance estimated in the support window versus the standard deviation of the disjoint noise.

Fig. 6
Fig. 6

(a) Matched filter correlation plane for Fig. 1, (b) matched filter correlation plane for Fig. 2, (c) LACIF correlation plane for Fig. 1, and (d) LACIF correlation plane for Fig. 2.

Equations (17)

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f ( x ) = a f ( x ) + b ( x ) ,
C lacif ( x ) = [ g ( x ) * f o ( x ) ] 2 [ g 2 ( x ) * ( x ) ] 1 N [ g ( x ) * ( x ) ] 2 ,
PSR = | C ( 0 ) | 2 max [ | C ( x ) | 2 ; ( x ) Σ { ( 0 ) } ] ,
s ( x ) = a f ( x ) ( x ) + D ( x ) [ 1 ( x ) ] ,
C cma = | [ a f ( x ) + D ( x ) ] * f ( x ) | 2 R f f 2 ,
C cma = | a R f f + R f D | 2 R f f 2 = a 2 ,
C cma D = R f D 2 R f f 2 ,
PSR cma = a 2 R f f 2 R f D 2 .
lim PSR cma σ D = lim a 2 R f f 2 R f D 2 σ D lim a 2 N σ f 2 σ D 2 σ D = 0 ,
C lacif D = R f o D 2 R f f N σ D 2 = R f o D 2 R f f R D D ,
PSR lacif = C lacif C lacif D = R f f R D D R f D 2 .
C lacif D + A = [ ( D + A ) * f o ] 2 N R f f σ D + A 2 = R D f o 2 + R A f o 2 N R f f σ D 2 + N R f f σ A 2 = R D f o 2 + R A f o 2 R f f R D D + R f f R A A .
P S R lacif = C lacif C lacif D + A = R f f R D D + R f f R A A R D f o 2 + R A f o 2 .
R f o D 2 < R f f R D D .
R f o A 2 < R f f R A A .
R f o D 2 + R f o A 2 < R f f R D D + R f f R A A .
lim PSR lacif σ A = lim N 2 σ f 2 σ D 2 + N 2 σ f 2 σ A 2 R f o D 2 + R f o A 2 σ A lim N 2 σ f 2 ( σ D 2 + σ A 2 ) ε σ A = .

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