Abstract

A scene-based nonuniformity correction algorithm is presented to compensate for the gain and bias nonuniformity in infrared focal-plane array sensors, which can be separated into three parts. First, an interframe-prediction method is used to estimate the true scene, since nonuniformity correction is a typical blind-estimation problem and both scene values and detector parameters are unavailable. Second, the estimated scene, along with its corresponding observed data obtained by detectors, is employed to update the gain and the bias by means of a line-fitting technique. Finally, with these nonuniformity parameters, the compensated output of each detector is obtained by computing a very simple formula. The advantages of the proposed algorithm lie in its low computational complexity and storage requirements and ability to capture temporal drifts in the nonuniformity parameters. The performance of every module is demonstrated with simulated and real infrared image sequences. Experimental results indicate that the proposed algorithm exhibits a superior correction effect.

© 2009 Optical Society of America

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  1. D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859 (1993).
    [CrossRef]
  2. Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
    [CrossRef]
  3. J. G. Harris and Y. M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
    [CrossRef]
  4. M. M. Hayat, S. N. Torres, E. Armstrong, S. C. Cain, and B. Yasuda, “Statistical algorithm for nonuniformity correction in focal-plane arrays,” Appl. Opt. 38, 772-780 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. J. E. Pezoa, M. M. Hayat, S. N. Torres, and M. S. Rahman, “Multimodel Kalman filtering for adaptive nonuniformity correction in infrared sensors,” J. Opt. Soc. Am. A 23, 1282-1291 (2006).
    [CrossRef]
  12. R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
    [CrossRef]
  13. B. E. Dunne and G. A. Williamson, “QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering,” IEEE Trans. Signal Process. 51, 386-394 (2003).
    [CrossRef]
  14. F. Torres, S. N. Torres, and C. San Martin, “A recursive least square adaptive filter for nonuniformity correction of infrared image sequences,” in Progress in Pattern Recognition, Image Analysis and Applications, Vol. 3773 ofLecture Notes in Computer Science (Springer, 2005), pp. 540-546.
    [CrossRef]
  15. C. Davila, “An efficient recursive total least squares algorithm for FIR adaptive filtering,” IEEE Trans. Signal Process. 42, 415-419 (1994).
    [CrossRef]
  16. G. Golub and C. V. Loan, Matrix Computations (Johns Hopkins U. Press, 1983).
  17. D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
    [CrossRef]
  18. J. G. Harris and Y. M. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
    [CrossRef]

2006 (1)

2005 (3)

2003 (3)

2002 (1)

2000 (1)

1999 (2)

M. M. Hayat, S. N. Torres, E. Armstrong, S. C. Cain, and B. Yasuda, “Statistical algorithm for nonuniformity correction in focal-plane arrays,” Appl. Opt. 38, 772-780 (1999).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

1998 (2)

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

1994 (1)

C. Davila, “An efficient recursive total least squares algorithm for FIR adaptive filtering,” IEEE Trans. Signal Process. 42, 415-419 (1994).
[CrossRef]

1993 (1)

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

1990 (1)

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Armstrong, E.

Armstrong, E. E.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Barnard, K. J.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Bognar, J. G.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Cain, S. C.

Cao, Z. G.

Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
[CrossRef]

Caulfield, J. T.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Chiang, Y. M.

J. G. Harris and Y. M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Davila, C.

C. Davila, “An efficient recursive total least squares algorithm for FIR adaptive filtering,” IEEE Trans. Signal Process. 42, 415-419 (1994).
[CrossRef]

Dereniak, E. L.

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

Dunne, B. E.

B. E. Dunne and G. A. Williamson, “QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering,” IEEE Trans. Signal Process. 51, 386-394 (2003).
[CrossRef]

Golub, G.

G. Golub and C. V. Loan, Matrix Computations (Johns Hopkins U. Press, 1983).

Gridley, C. J.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Hardie, R. C.

Harris, J. G.

J. G. Harris and Y. M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Hayat, M. M.

Katz, G.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Kruer, M. R.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Li, H.

Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
[CrossRef]

Loan, C. V.

G. Golub and C. V. Loan, Matrix Computations (Johns Hopkins U. Press, 1983).

Muse, R. A.

Narayanan, B.

Perry, D. L.

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

Pezoa, J. E.

Rahman, M. S.

Ratliff, B. M.

San Martin, C.

F. Torres, S. N. Torres, and C. San Martin, “A recursive least square adaptive filter for nonuniformity correction of infrared image sequences,” in Progress in Pattern Recognition, Image Analysis and Applications, Vol. 3773 ofLecture Notes in Computer Science (Springer, 2005), pp. 540-546.
[CrossRef]

Sarkady, K. A.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Scribner, D. A.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Shi, Y.

Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
[CrossRef]

Torres, F.

F. Torres, S. N. Torres, and C. San Martin, “A recursive least square adaptive filter for nonuniformity correction of infrared image sequences,” in Progress in Pattern Recognition, Image Analysis and Applications, Vol. 3773 ofLecture Notes in Computer Science (Springer, 2005), pp. 540-546.
[CrossRef]

Torres, S. N.

Tyo, J. S.

Watson, E. A.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Williamson, G. A.

B. E. Dunne and G. A. Williamson, “QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering,” IEEE Trans. Signal Process. 51, 386-394 (2003).
[CrossRef]

Yasuda, B.

Zhang, T. X.

Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Image Process. (1)

J. G. Harris and Y. M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

IEEE Trans. Signal Process. (2)

B. E. Dunne and G. A. Williamson, “QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering,” IEEE Trans. Signal Process. 51, 386-394 (2003).
[CrossRef]

C. Davila, “An efficient recursive total least squares algorithm for FIR adaptive filtering,” IEEE Trans. Signal Process. 42, 415-419 (1994).
[CrossRef]

Infrared Phys. Technol. (1)

Y. Shi, T. X. Zhang, Z. G. Cao, and H. Li, “A feasible approach for nonuniformity correction in IRFPA with nonlinear response,” Infrared Phys. Technol. 46, 329-337 (2005).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Eng. (2)

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Proc. SPIE (2)

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridley, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Other (2)

G. Golub and C. V. Loan, Matrix Computations (Johns Hopkins U. Press, 1983).

F. Torres, S. N. Torres, and C. San Martin, “A recursive least square adaptive filter for nonuniformity correction of infrared image sequences,” in Progress in Pattern Recognition, Image Analysis and Applications, Vol. 3773 ofLecture Notes in Computer Science (Springer, 2005), pp. 540-546.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the proposed NUC algorithm.

Fig. 2
Fig. 2

(a) Shifted infrared image. (b) Infrared image with simulated nonuniformity.

Fig. 3
Fig. 3

ARE for various levels of gain and bias nonuniformity ( σ a denotes gain standard deviation and σ b bias standard deviation).

Fig. 4
Fig. 4

(a) True image of frame 181. (b) Image estimated from frame 180.

Fig. 5
Fig. 5

Performance of interframe prediction versus frame number.

Fig. 6
Fig. 6

Relationships between input and output before and after corruption.

Fig. 7
Fig. 7

Average line-fitting results against frame number. (a) Parameter a estimated by RLS and RMLS. (b) Parameter b estimated by RLS and RMLS.

Fig. 8
Fig. 8

Correction performances of RLS and RMLS against frame number with real infrared data.

Fig. 9
Fig. 9

(a) Original image of frame 200. (b) Image corrected by RLS. (c) Image corrected by RMLS.

Equations (30)

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y k ( i , j ) = a k ( i , j ) x k ( i , j ) + b k ( i , j ) ,
x k + 1 ( i , j ) = x k ( i + h k , j + v k ) .
x k + 1 ( i , j ) x k ( i , j ) + h k g k i ( i , j ) + v k g k j ( i , j ) ,
h ^ k , v ^ k = argmin h k , v k E k ( h k , v k ) ,
E k ( h k , v k ) = i = 1 M j = 1 N [ x k + 1 ( i , j ) x k ( i , j ) h k g k i ( i , j ) v k g k j ( i , j ) ] 2 .
[ h ^ k v ^ k ] = [ i = 1 M j = 1 N [ g k i ( i , j ) ] 2 i = 1 M j = 1 N g k i ( i , j ) g k j ( i , j ) i = 1 M j = 1 N g k i ( i , j ) g k j ( i , j ) i = 1 M j = 1 N [ g k j ( i , j ) ] 2 ] 1 × [ i = 1 M j = 1 N Δ X k ( i , j ) g k i ( i , j ) i = 1 M j = 1 N Δ X k ( i , j ) g k j ( i , j ) ] ,
Δ X k ( i , j ) = x k + 1 ( i , j ) x k ( i , j ) .
x ^ k + 1 ( i , j ) = γ 1 , k x k ( i + h ^ k + 1 , j + v ^ k + 1 ) + γ 2 , k x k ( i + h ^ k + 1 , j + v ^ k ) + γ 3 , k x k ( i + h ^ k , j + v ^ k + 1 ) + γ 4 , k x k ( i + h ^ k , j + v ^ k ) ,
y k = a k x k + b k .
Δ y k = y k y ^ k = y k H k θ ^ k ,
Δ y ( k ) = y ( k ) y ^ ( k ) = y ( k ) H ( k ) θ ^ k ,
ε k = n = 1 k ( y n H n θ ^ k ) 2 .
θ ^ k = [ H T ( k ) H ( k ) ] 1 H T ( k ) y ( k ) = P k H T ( k ) y ( k ) ,
θ ^ k + 1 = θ ^ k + K k + 1 [ y k + 1 H k + 1 θ ^ k ] ,
K k + 1 = P k + 1 H k + 1 T ,
P k + 1 = P k P k H k + 1 T H k + 1 P k 1 + H k + 1 P k H k + 1 T ,
{ min [ Δ x ( k ) Δ y ( k ) ] F subject to [ W ( k ) + Δ W ( k ) ] γ k = [ 1 y ( k ) - Δ y ( k ) x ^ ( k ) Δ x ( k ) ] γ k = 0 ,
min γ k { γ k T R ^ W W ( k ) γ k γ k T γ k } ,
R ^ W W ( k ) = 1 k W T ( k ) W ( k ) .
W ( k ) = Q ( k ) R ¯ ( k ) ,
[ R ( k + 1 ) 0 ] = T ( k + 1 ) [ R ( k ) W k + 1 ] ,
W T ( k + 1 ) W ( k + 1 ) = [ W T ( k ) W k + 1 T ] [ W ( k ) W k + 1 ] = R ¯ T ( k ) R ¯ ( k ) + W k + 1 T W k + 1 = R T ( k ) R ( k ) + W k + 1 T W k + 1 = R T ( k + 1 ) R ( k + 1 ) .
min γ k { γ k T R T ( k ) R ( k ) γ k γ k T γ k } .
R ( k ) = [ R 11 ( k ) R 1 y ( k ) R 12 ( k ) 0 R 2 y ( k ) R 22 ( k ) ] ,
R 2 ( k ) γ ^ k = [ R 2 y ( k ) R 22 ( k ) ] [ 1 a ^ k ] = 0 ,
[ R 11 ( k ) R 1 y ( k ) R 12 ( k ) ] γ ^ k = R 11 ( k ) b ^ k R 1 y ( k ) + R 12 ( k ) a ^ k = 0.
x ˜ k = y k b ^ k a ^ k .
y = 2 x + 5 ,
δ k = i = 1 M j = 1 N | y k ( i , j ) y k 1 ( i , j ) | .
ρ ( f ) = | | h 1 * f | | 1 + | | h 2 * f | | 1 | | f | | 1 ,

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