Abstract

The design of an optimum receiver for pattern-recognition problems with input scene noise that is spatially disjoint (nonoverlapping) with the target is described. The processor is designed based on multiple alternative-hypothesis testing.

© 1993 Optical Society of America

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References

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  1. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).
  2. D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
    [CrossRef]
  3. B. Javidi, J. Wang, Appl. Opt. 31, 6826 (1992).
    [CrossRef] [PubMed]
  4. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).
  5. F. M. Dickey, L. A. Romero, Opt. Lett. 16, 1186 (1991).
    [CrossRef] [PubMed]

1992

1991

1989

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[CrossRef]

1964

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

Dickey, F. M.

Flannery, D. L.

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[CrossRef]

Horner, J. L.

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[CrossRef]

Javidi, B.

Romero, L. A.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

Wang, J.

Appl. Opt.

IEEE Trans. Inf. Theory

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

Opt. Lett.

Proc. IEEE

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[CrossRef]

Other

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

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Figures (1)

Fig. 1
Fig. 1

(a) Target (tank) with unknown illumination in nonoverlapping background noise used in the tests. (b) Example of the test function [−CN(tj)] for the target in the presence of spatially disjoint background noise shown in (a). CN(tj) is given by Eq. (5). (c) Classic correlation receiver solution i = 1 m r ( t i ) s ( t i t j ) for the target in the presence of spatially disjoint background noise shown in (a). The figure illustrates the pixels around the correlation peak. The correlation peak cannot be seen because it is below the output noise floor.

Equations (9)

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r ( t ) = [ a s ( t t j ) + n d ( t ) ] w ( t t j ) + n j ( t ) .
p n d ( n d ) = i = 1 m s p n d [ n d ( t i ) ] = [ ( 1 / 2 π σ d 2 ) 0.5 m s ] × exp { i = 1 m s [ n d ( t i ) ] 2 / 2 σ d 2 } .
log [ p ( r / H j ; a ) ] = log [ p n j ( r j ¯ ) ] ( 1 / 2 σ d 2 ) × i = 1 m w ( t i t j ) [ r ( t i ) a s ( t i t j ) ] 2 + 0.5 m s log ( 1 / 2 π σ d 2 ) .
i = 1 m [ r ( t i ) â s ( t i t j ) ] s ( t i t j ) = 0
â = i = 1 m r ( t i ) s ( t i t j ) / i = 1 m s 2 ( t i t j ) ,
log [ p ( r / H j ; â ) ] = log [ p n j ( r j ¯ ) ] ( 1 / 2 σ d 2 ) × i = 1 m w ( t i t j ) [ r ( t i ) â s ( t i t j ) ] 2 ,
log [ p ( r / H j ; â ) ] = log [ p n j ( r j ¯ ) ] ( 1 / 2 σ d 2 ) C N ( t j ) ; C N ( t j ) = i = 1 m r 2 ( t i ) w ( t i t j ) [ i = 1 m r ( t i ) s ( t i t j ) ] 2 / i = 1 m s 2 ( t i t j ) .
M j ( r ) = [ i = 1 m r ( t i ) s ( t i t j ) ] 2 / [ i = 1 m s 2 ( t i t j ) i = 1 m r 2 ( t i ) w ( t i t j ) ] 1 .
log [ p ( r / H j ; â ) ] = [ 1 / 2 ( σ n 2 + σ d 2 ) ] × i = 1 n { [ 1 w ( t i t j ) ] r ( t i ) m n } 2 ( 1 / 2 σ d 2 ) C N ( t j ) .

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