Abstract

A statistical algorithm has been developed to compensate for the fixed-pattern noise associated with spatial nonuniformity and temporal drift in the response of focal-plane array infrared imaging systems. The algorithm uses initial scene data to generate initial estimates of the gain, the offset, and the variance of the additive electronic noise of each detector element. The algorithm then updates these parameters by use of subsequent frames and uses the updated parameters to restore the true image by use of a least-mean-square error finite-impulse-response filter. The algorithm is applied to infrared data, and the restored images compare favorably with those restored by use of a multiple-point calibration technique.

© 1999 Optical Society of America

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  1. A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
    [CrossRef]
  2. G. C. Holst, CCD Arrays, Cameras, and Displays, Vol. PM57 of SPIE Monographs and Handbook Series (SPIE, Bellingham, Wash., 1996).
  3. D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).
  4. D. A. Scribner, M. R. Kruer, J. C. Gridley, “Physical limitations to nonuniformity correction in focal plane arrays,” in Focal Plane Arrays: Technology and Applications, J. P. Chatard, ed., Proc. SPIE865, 185–201 (1988).
    [CrossRef]
  5. D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1853–1859 (1993).
    [CrossRef]
  6. M. Schulz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763–777 (1995).
    [CrossRef]
  7. D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
    [CrossRef]
  8. D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).
  9. P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
    [CrossRef]
  10. J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
    [CrossRef]
  11. J. G. Harris, Y.-M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Anderson, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
    [CrossRef]
  12. S. Cain, E. Armstrong, B. Yasuda, “Joint estimation of image, shifts, and nonuniformities from IR images,” in Proceedings of the 1997 Meeting of the Infrared Information Symposium (IRIS) Specialty Group on Passive Sensors (Infrared Information Analysis Center, ERIM International, Ann Arbor, Mich., 1997).
  13. H. V. Poor, Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1988).
    [CrossRef]
  14. H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1994).

1995

M. Schulz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763–777 (1995).
[CrossRef]

1993

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1853–1859 (1993).
[CrossRef]

1985

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
[CrossRef]

Armstrong, E.

S. Cain, E. Armstrong, B. Yasuda, “Joint estimation of image, shifts, and nonuniformities from IR images,” in Proceedings of the 1997 Meeting of the Infrared Information Symposium (IRIS) Specialty Group on Passive Sensors (Infrared Information Analysis Center, ERIM International, Ann Arbor, Mich., 1997).

Barone, F. R.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
[CrossRef]

Cain, S.

S. Cain, E. Armstrong, B. Yasuda, “Joint estimation of image, shifts, and nonuniformities from IR images,” in Proceedings of the 1997 Meeting of the Infrared Information Symposium (IRIS) Specialty Group on Passive Sensors (Infrared Information Analysis Center, ERIM International, Ann Arbor, Mich., 1997).

Caldwell, L.

M. Schulz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763–777 (1995).
[CrossRef]

Calufield, J.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Calufield, J. T.

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

Caulfield, J. T.

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

Chiang, Y.-M.

J. G. Harris, Y.-M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Anderson, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

Colbert, M.

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Dereniak, E. L.

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1853–1859 (1993).
[CrossRef]

Descour, M.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

Foss, N. A.

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

Gridley, C. J.

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

Gridley, J. C.

D. A. Scribner, M. R. Kruer, J. C. Gridley, “Physical limitations to nonuniformity correction in focal plane arrays,” in Focal Plane Arrays: Technology and Applications, J. P. Chatard, ed., Proc. SPIE865, 185–201 (1988).
[CrossRef]

Harris, J. G.

J. G. Harris, Y.-M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Anderson, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
[CrossRef]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays, Vol. PM57 of SPIE Monographs and Handbook Series (SPIE, Bellingham, Wash., 1996).

Hunt, J.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Hunt, J. D.

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

Katz, G.

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

Kruer, M.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Kruer, M. R.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
[CrossRef]

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

D. A. Scribner, M. R. Kruer, J. C. Gridley, “Physical limitations to nonuniformity correction in focal plane arrays,” in Focal Plane Arrays: Technology and Applications, J. P. Chatard, ed., Proc. SPIE865, 185–201 (1988).
[CrossRef]

Milton, A. F.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
[CrossRef]

Narendra, P. M.

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

Perry, D. L.

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1853–1859 (1993).
[CrossRef]

Poor, H. V.

H. V. Poor, Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1988).
[CrossRef]

Sarkady, K.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Sarkady, K. A.

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

Sarkay, K. A.

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

Schulz, M.

M. Schulz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763–777 (1995).
[CrossRef]

Scribner, D.

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

Scribner, D. A.

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

D. A. Scribner, M. R. Kruer, J. C. Gridley, “Physical limitations to nonuniformity correction in focal plane arrays,” in Focal Plane Arrays: Technology and Applications, J. P. Chatard, ed., Proc. SPIE865, 185–201 (1988).
[CrossRef]

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

Stark, H.

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Woods, J. W.

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Yasuda, B.

S. Cain, E. Armstrong, B. Yasuda, “Joint estimation of image, shifts, and nonuniformities from IR images,” in Proceedings of the 1997 Meeting of the Infrared Information Symposium (IRIS) Specialty Group on Passive Sensors (Infrared Information Analysis Center, ERIM International, Ann Arbor, Mich., 1997).

Infrared Phys. Technol.

M. Schulz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763–777 (1995).
[CrossRef]

Opt. Eng.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
[CrossRef]

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1853–1859 (1993).
[CrossRef]

Other

G. C. Holst, CCD Arrays, Cameras, and Displays, Vol. PM57 of SPIE Monographs and Handbook Series (SPIE, Bellingham, Wash., 1996).

D. A. Scribner, K. A. Sarkay, J. T. Caulfield, M. R. Kruer, G. Katz, C. J. Gridley, “Nonuniformity correction for staring focal plane arrays using scene-based techniques,” in Infrared Detectors and Focal Plane Arrays, E. Dereniak, R. E. Sampson, eds., Proc. SPIE1308, 224–233 (1990).

D. A. Scribner, M. R. Kruer, J. C. Gridley, “Physical limitations to nonuniformity correction in focal plane arrays,” in Focal Plane Arrays: Technology and Applications, J. P. Chatard, ed., Proc. SPIE865, 185–201 (1988).
[CrossRef]

D. A. Scribner, K. A. Sarkady, M. R. Kruer, J. T. Calufield, J. D. Hunt, M. Colbert, M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 1955–1960.
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Calufield, J. Hunt, M. Colbert, M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” in Infrared Sensors: Detectors, Electronics, and Signal Processing, T. S. Jayadev, ed., Proc. SPIE1541, 100–109 (1991).

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
[CrossRef]

J. G. Harris, Y.-M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Anderson, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

S. Cain, E. Armstrong, B. Yasuda, “Joint estimation of image, shifts, and nonuniformities from IR images,” in Proceedings of the 1997 Meeting of the Infrared Information Symposium (IRIS) Specialty Group on Passive Sensors (Infrared Information Analysis Center, ERIM International, Ann Arbor, Mich., 1997).

H. V. Poor, Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1988).
[CrossRef]

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1994).

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the statistical NUC algorithm.

Fig. 2
Fig. 2

Single frame from the uncorrected first data set.

Fig. 3
Fig. 3

Single frame from the uncorrected second data set.

Fig. 4
Fig. 4

Frame from Fig. 2 but with NUC by use of the initial estimates of the gain, the offset, and the noise variance.

Fig. 5
Fig. 5

Corrected version of the image of Fig. 2 obtained by use of the updated gain and offset. Note the improvement, which is due to recursion, in the correction compared with that of the image of Fig. 4.

Fig. 6
Fig. 6

Corrected version of the frame of Fig. 2 obtained by use of a multiple-point calibration method.

Fig. 7
Fig. 7

Corrected version of the scene from Fig. 3 obtained by use of the updated gain and offset.

Fig. 8
Fig. 8

Corrected version of the frame of Fig. 3 obtained by use of a multiple-point calibration method.

Fig. 9
Fig. 9

Corrected version of the frame of Fig. 3 obtained by use of the new algorithm but with use of the gain and the offset that correspond to data set 1. The advantage of updating the gain and the offset is evident compared with the image of Fig. 7.

Tables (2)

Tables Icon

Table 1 Performance Parameter ρ for Data Set 1

Tables Icon

Table 2 Performance Parameter ρ for Data Set 2

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

Yijn=AijnXijn+Bijn+Nijn,
Ymax0  max-npn-1Yn, Ymin0  min-npn-1Yn.
Ymax0A0max-npn-1Xn+B0,
Ymin0A0min-npn-1Xn+B0.
max-npn-1Xnxmax, min-npn-1Xnxmin,
A0=Ymax0-Ymin0xmax-xmin,
B0=Ymax0-A0xmax.
DnNn-Nn-1.
σN,02=121npn=-np-1Dn-Dˆ02,
Dˆ0  1npn=-np-1 Dn.
Xˆn=i=n-L+1n wkiYi+β,
EXˆn-Xn2.
Wk=CYYk-1CXYk,
β=μX-AkμX+Bki=1L wki,
CXYk=CXXkAk,
CYYk=Ak2CXXk+σN,k2I,
Wk=AkσX2Ak2σX2+σN,k2 β=μX-wkAkμX+Bk,
σX2=112xmax-xmin2
σN,k2121npn=knb-npknb-1Dn-Dˆk2,
Dˆk  1npn=knb-npknb-1 Dn.
yˆk  1npn=knb-npknb-1 Yn,
σY2ˆk  1npn=knb-npknb-1Yi-yˆk2,
yˆkAkμXk+Bk,
σY2ˆkAk2σX2k+σN,k2.
μXˆk=xmaxk+xmink/2,
σX2ˆk=xmaxk-xmink2/12.
ρf  h1 * f1+h2 * f1f1,

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