Abstract

A composite filter is designed for distortion-invariant detection of a target in the presence of nonoverlapping scene noise. The performance of the filter is illustrated by the use of computer simulation for the in-plane rotation of a target in nonoverlapping scene noise.

© 1995 Optical Society of America

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References

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1994 (1)

1993 (1)

1992 (2)

B. Javidi, J. Wang, Appl. Opt. 31, 6828 (1992).

B. V. K. V. Kumar, Appl. Opt. 31, 4773 (1992).
[CrossRef] [PubMed]

1984 (1)

1976 (1)

1969 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

1960 (1)

J. L. Turin, IRE Trans. Inf. Theory IT-6, 311 (1960).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Reference target: a car. (b) The false-class object: an airplane.

Fig. 2
Fig. 2

Output measurements for true-class targets and false-class objects in nonoverlapping scene noise for (a) the POE and (b) the peak intensity. Each test was repeated 20 times to yield the statistical averages. In (a) the asterisks represent the ratio of the square of the expected value of the output signal at the target location to the expected value of the output energy and the circles represent the ratio of the square of the expected value of the maximum value of the output to the expected value of the output energy. In (b) the solid curve represents the expected value of the maximum output intensity for 20 trials. The dashed curve is the expected value of the output intensity at the target location for 20 trials. The length of the vertical bar on each measurement represents the standard deviation of the corresponding peak intensity.

Equations (14)

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s i ( t ) = r i ( t - τ ) + n b ( t ) [ w 0 ( t ) - w r i ( t - τ ) ] ,
H i * ( ω ) = R i ( ω ) + m n W ˜ 1 i ( ω ) | R i ( ω ) + m b W ˜ 1 i ( ω ) | 2 + 1 2 π W ˜ 2 i ( ω ) * S n ( ω ) - m n 2 | W ˜ 1 i ( ω ) | 2 ,             i = 1 , N ,
W ˜ 1 i ( ω ) = | W 0 ( ω ) | 2 / d - W r i ( ω ) ,
W ˜ 2 i ( ω ) = | W 0 ( ω ) | 2 + | W r i ( ω ) | 2 - 2 | W 0 ( ω ) | 2 Re [ W r i ( ω ) ] / d ,
d = W 0 ( 0 ) = w 0 ( t ) d t .
H c ( ω ) = k = 1 N a k H k ( ω ) .
H c ( ω ) = H ( ω ) A ,
H _ ( ω ) = [ H 1 ( ω ) H 2 ( ω ) H N ( ω ) ] ,
A = [ a 1 a 2 a N ] T .
E [ H c ( ω ) S i ( ω ) exp ( j ω τ ) d ω ] = c i ,     i = 1 , , N ,
p i k = E [ S i ( ω ) exp ( j ω τ ) ] H k ( ω ) d ω .
P A = C
A = P - 1 C ,
H c ( ω ) = H _ ( ω ) P - 1 C ,

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