Abstract

What is to our knowledge a new scene-based algorithm for nonuniformity correction in infrared focal-plane array sensors has been developed. The technique is based on the inverse covariance form of the Kalman filter (KF), which has been reported previously and used in estimating the gain and bias of each detector in the array from scene data. The gain and the bias of each detector in the focal-plane array are assumed constant within a given sequence of frames, corresponding to a certain time and operational conditions, but they are allowed to randomly drift from one sequence to another following a discrete-time Gauss-Markov process. The inverse covariance form filter estimates the gain and the bias of each detector in the focal-plane array and optimally updates them as they drift in time. The estimation is performed with considerably higher computational efficiency than the equivalent KF. The ability of the algorithm in compensating for fixed-pattern noise in infrared imagery and in reducing the computational complexity is demonstrated by use of both simulated and real data.

© 2003 Optical Society of America

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References

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  1. G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).
  2. P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
    [CrossRef]
  3. 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]
  4. P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
    [CrossRef]
  5. 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]
  6. 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. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
    [CrossRef]
  7. J. G. Harris, Y-M Chiang, “Minimizing the ‘ghosting’ artifact in scene-based nonuniformity correction,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing IX, G. C. Holst, ed., Proc. SPIE3377, 106–113 (1998).
    [CrossRef]
  8. J. G. Harris, Y-M Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148–1151 (1999).
    [CrossRef]
  9. Y.-M. Chiang, J. G. Harris, “An analog integrated circuit for continuous-time gain and offset calibration of sensor arrays,” J. Analog Int. Circuits Signal Process. 12, 231–238 (1997).
    [CrossRef]
  10. W. F. O’Neil, “Experimental verification of dithered scan non-uniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Michigan, 1997), Vol. 1, pp. 329–339.
  11. R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
    [CrossRef]
  12. B. M. Ratliff, M. M. Hayat, R. C. Hardie, “An algebraic algorithm for nonuniformity correction in focal-pane arrays,” J. Opt. Soc. Am. A 19, 1737–1747 (2002).
    [CrossRef]
  13. K. C. Hepfer, S. R. Horman, B. Horsch, “Method and device for improved IR detection with compensations for individual detector response,” U.S. patent5,276,319 (4January1994).
  14. M. M. Hayat, S. Torres, E. E. Armstrong, B. Yasuda, S. C. Cain, “Statistical algorithm for non-uniformity correction in focal plane arrays,” Appl. Opt. 38, 772–780 (1999).
    [CrossRef]
  15. E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
    [CrossRef]
  16. S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
    [CrossRef]
  17. S. N. Torres, M. M. Hayat, “Kalman filtering for adaptive nonuniformity correction in infrared focal plane arrays,” J. Opt. Soc. Am. A 20, 470–480 (2003).
    [CrossRef]
  18. G. Minkler, J. Minkler, Theory and Applications of Kalman Filtering (Magellan, Palm Bay, Fla., 1993).
  19. C. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992).
  20. S. N. Torres, “A Kalman filtering approach for non-uniformity correction in infrared focal plane array sensors,” Ph.D. dissertation (University of Dayton, Ohio, 2001).
  21. M. Schultz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing VI, G. C. Hulst, ed. Proc. SPIE2470, 200–211 (1995).
    [CrossRef]
  22. Z. Wang, A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
    [CrossRef]
  23. J. L. Hennessy, D. A. Patterson, Computer Organization and Design: The Hardware/Software Interface (Morgan Kaufmann, Los Altos, Calif., 1997).

2003 (1)

2002 (2)

2000 (1)

1999 (2)

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

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

1997 (1)

Y.-M. Chiang, J. G. Harris, “An analog integrated circuit for continuous-time gain and offset calibration of sensor arrays,” J. Analog Int. Circuits Signal Process. 12, 231–238 (1997).
[CrossRef]

Armstrong, E. E.

R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
[CrossRef]

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

S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
[CrossRef]

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

Bovik, A.

Z. Wang, A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Cain, S. C.

Caldwell, L.

M. Schultz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing VI, G. C. Hulst, ed. Proc. SPIE2470, 200–211 (1995).
[CrossRef]

Chatard, J. P.

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[CrossRef]

Chiang, Y.-M.

Y.-M. Chiang, J. G. Harris, “An analog integrated circuit for continuous-time gain and offset calibration of sensor arrays,” J. Analog Int. Circuits Signal Process. 12, 231–238 (1997).
[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. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

Chiang, Y-M

J. G. Harris, 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, Y-M Chiang, “Minimizing the ‘ghosting’ artifact in scene-based nonuniformity correction,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing IX, G. C. Holst, ed., Proc. SPIE3377, 106–113 (1998).
[CrossRef]

Chorier, P.

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[CrossRef]

Costa, P.

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[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]

Hardie, R. C.

B. M. Ratliff, M. M. Hayat, R. C. Hardie, “An algebraic algorithm for nonuniformity correction in focal-pane arrays,” J. Opt. Soc. Am. A 19, 1737–1747 (2002).
[CrossRef]

R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
[CrossRef]

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

Harris, J. G.

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

Y.-M. Chiang, J. G. Harris, “An analog integrated circuit for continuous-time gain and offset calibration of sensor arrays,” J. Analog Int. Circuits Signal Process. 12, 231–238 (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]

J. G. Harris, Y-M Chiang, “Minimizing the ‘ghosting’ artifact in scene-based nonuniformity correction,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing IX, G. C. Holst, ed., Proc. SPIE3377, 106–113 (1998).
[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. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

Hayat, M. M.

S. N. Torres, M. M. Hayat, “Kalman filtering for adaptive nonuniformity correction in infrared focal plane arrays,” J. Opt. Soc. Am. A 20, 470–480 (2003).
[CrossRef]

B. M. Ratliff, M. M. Hayat, R. C. Hardie, “An algebraic algorithm for nonuniformity correction in focal-pane arrays,” J. Opt. Soc. Am. A 19, 1737–1747 (2002).
[CrossRef]

R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
[CrossRef]

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

S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
[CrossRef]

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

Hennessy, J. L.

J. L. Hennessy, D. A. Patterson, Computer Organization and Design: The Hardware/Software Interface (Morgan Kaufmann, Los Altos, Calif., 1997).

Hepfer, K. C.

K. C. Hepfer, S. R. Horman, B. Horsch, “Method and device for improved IR detection with compensations for individual detector response,” U.S. patent5,276,319 (4January1994).

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

Horman, S. R.

K. C. Hepfer, S. R. Horman, B. Horsch, “Method and device for improved IR detection with compensations for individual detector response,” U.S. patent5,276,319 (4January1994).

Horsch, B.

K. C. Hepfer, S. R. Horman, B. Horsch, “Method and device for improved IR detection with compensations for individual detector response,” U.S. patent5,276,319 (4January1994).

Manissadjian, A.

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[CrossRef]

Minkler, G.

G. Minkler, J. Minkler, Theory and Applications of Kalman Filtering (Magellan, Palm Bay, Fla., 1993).

Minkler, J.

G. Minkler, J. Minkler, Theory and Applications of Kalman Filtering (Magellan, Palm Bay, Fla., 1993).

Narendra, P. M.

P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
[CrossRef]

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]

O’Neil, W. F.

W. F. O’Neil, “Experimental verification of dithered scan non-uniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Michigan, 1997), Vol. 1, pp. 329–339.

Patterson, D. A.

J. L. Hennessy, D. A. Patterson, Computer Organization and Design: The Hardware/Software Interface (Morgan Kaufmann, Los Altos, Calif., 1997).

Ratliff, B. M.

Schultz, M.

M. Schultz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing VI, G. C. Hulst, ed. Proc. SPIE2470, 200–211 (1995).
[CrossRef]

Therrien, C.

C. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992).

Torres, S.

Torres, S. N.

S. N. Torres, M. M. Hayat, “Kalman filtering for adaptive nonuniformity correction in infrared focal plane arrays,” J. Opt. Soc. Am. A 20, 470–480 (2003).
[CrossRef]

S. N. Torres, “A Kalman filtering approach for non-uniformity correction in infrared focal plane array sensors,” Ph.D. dissertation (University of Dayton, Ohio, 2001).

S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
[CrossRef]

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

Tribolet, P.

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[CrossRef]

Wang, Z.

Z. Wang, A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Yasuda, B.

R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
[CrossRef]

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

S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
[CrossRef]

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

Appl. Opt. (2)

IEEE Signal Process. Lett. (1)

Z. Wang, A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

IEEE Trans. Image Process. (1)

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

J. Analog Int. Circuits Signal Process. (1)

Y.-M. Chiang, J. G. Harris, “An analog integrated circuit for continuous-time gain and offset calibration of sensor arrays,” J. Analog Int. Circuits Signal Process. 12, 231–238 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

Other (16)

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

P. Tribolet, P. Chorier, A. Manissadjian, P. Costa, J. P. Chatard, “High performance infrared detectors at Sofradir,” in Infrared Detectors and Focal Pane Arrays VI, E. L. Dereniak, R. E. Sampson, eds., Proc. SPIE4028, 438–456 (2002).
[CrossRef]

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]

P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
[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. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

J. G. Harris, Y-M Chiang, “Minimizing the ‘ghosting’ artifact in scene-based nonuniformity correction,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing IX, G. C. Holst, ed., Proc. SPIE3377, 106–113 (1998).
[CrossRef]

W. F. O’Neil, “Experimental verification of dithered scan non-uniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Michigan, 1997), Vol. 1, pp. 329–339.

K. C. Hepfer, S. R. Horman, B. Horsch, “Method and device for improved IR detection with compensations for individual detector response,” U.S. patent5,276,319 (4January1994).

E. E. Armstrong, M. M. Hayat, R. C. Hardie, S. N. Torres, B. Yasuda, “Nonuniformity correction for improved registration and high resolution image reconstruction in IR imagery,” in Applications of Digital Image Processing XXII, A. G. Tescher, ed., Proc. SPIE3808, 150–161 (1999).
[CrossRef]

S. N. Torres, M. M. Hayat, E. E. Armstrong, B. Yasuda, “A Kalman-filtering approach for nonuniformity correction in focal-plane array sensors,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XI, G. C. Hulst, ed., Proc. SPIE4030, 196–205 (2000).
[CrossRef]

G. Minkler, J. Minkler, Theory and Applications of Kalman Filtering (Magellan, Palm Bay, Fla., 1993).

C. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992).

S. N. Torres, “A Kalman filtering approach for non-uniformity correction in infrared focal plane array sensors,” Ph.D. dissertation (University of Dayton, Ohio, 2001).

M. Schultz, L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing VI, G. C. Hulst, ed. Proc. SPIE2470, 200–211 (1995).
[CrossRef]

J. L. Hennessy, D. A. Patterson, Computer Organization and Design: The Hardware/Software Interface (Morgan Kaufmann, Los Altos, Calif., 1997).

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Figures (15)

Fig. 1
Fig. 1

Infrared imagery from the fifth block.

Fig. 2
Fig. 2

Image of Fig. 1 corrupted with simulated nonuniformity generated with standard deviations of 0.10 and 10 for the gain and the bias, respectively.

Fig. 3
Fig. 3

MSE of the gain and the bias as a function of the level of nonuniformity generated mainly by the gain. The standard deviation for the bias is 5 (relative to an 8-bit scale). Open circles represent low drift (α k = β k = 0.95), open squares represent moderate drift (α k = β k = 0.7), and the asterisks represent high drift (α k = β k = 0.3).

Fig. 4
Fig. 4

Roughness parameter, ρ, and the Q index as a function of the level of gain-dominated nonuniformity. The bias standard deviation is fixed at 5. Open circles represent low drift (α k = β k = 0.95), open squares represent moderate drift (α k = β k = 0.7), and the asterisks represent high drift (α k = β k = 0.3). Open diamonds represent the corresponding parameters for the uncorrected block.

Fig. 5
Fig. 5

Frame of Fig. 1 corrected by use of the traditional KF.

Fig. 6
Fig. 6

Frame of Fig. 1 corrected by use of the ICF Filter.

Fig. 7
Fig. 7

CPU time consumed by the traditional KF and the ICF filter as a function of the block index k. Open circles and crosses represent the CPU time consumed by the traditional Kalman and the ICF filters, respectively. The dotted curve represents a frame size of 32 × 32 pixels, the solid curve represents the case of 64 × 64 pixels, and the dashed-dotted curve represents the case of 128 × 128 pixels.

Fig. 8
Fig. 8

Infrared imagery from block 5.

Fig. 9
Fig. 9

Frame of Fig. 8 corrected by use of 500 consecutive frames per block with the drift factors taken as α5 = β5 = 0.95.

Fig. 10
Fig. 10

Imagery from the first block (corresponding to 6:30 AM).

Fig. 11
Fig. 11

Frame of Fig. 10 corrected by use of 500 consecutive frames per block and correlation factors α1 = β1 = 0.95.

Fig. 12
Fig. 12

Frame of Fig. 10 corrected by use of 500 consecutive frames per block, for which we stipulate that the first block arrives after the fourth block (in place of the existing fifth block). The drift factors are taken as α5 = β5 = 0.95.

Fig. 13
Fig. 13

Imagery from the sixth block.

Fig. 14
Fig. 14

Frame of Fig. 13 corrected by use of 500 consecutive frames per block and correlation factors α6 = β6 = 0.95.

Fig. 15
Fig. 15

Frame of Fig. 13 corrected by use of 800 consecutive frames per block and correlation factors α6 = β6 = 0.8.

Tables (2)

Tables Icon

Table 1 Number of Operations (per Pixel and per Block of Frames)a

Tables Icon

Table 2 Performance Parameters MSE, RMSE, ρ, and Q at the k = 5 blocka

Equations (23)

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

Ykijn=AkijTkijn+Bkij+Vkijn,
Ak+1Bk+1=αk00βkAkBk+1001Wk1Wk2,
Xk+1=ΦkXk+GkWk.
Yk1Yklk=Tk11Tklk1AkBk+Vk1Vklk
Yk=HkXk+Vk,
Xˆk¯=Φk-1Xˆk-1+Mk-1T,
Pk¯=Φk-1Pk-1Φk-1T+Gk-1Qk-1Gk-1T,
Kk=Pk¯H¯kTH¯kPk¯H¯kT+Sk-1,
Sk=Rk+σTk2σA02+A¯0Ilk,lk,
Xˆk=Xˆk¯+KkYk-H¯kXˆk¯,
Pk=I2,2-KkH¯kPk¯,
Xˆ0=EX0=A¯0B¯0, P0=Λ=σA0200σB02.
aˆk  Pk-1Xˆk,
aˆk¯=I2,2-Dk-1Gk-1TΦk-1-1aˆk-1+Ck-1Mk-1T,
Pk¯-1=I2,2-Dk-1Gk-1TCk-1,
Ck-1  Φk-1-TPk-1-1Φk-1-1,
Dk-1  Ck-1Gk-1Qk-1-1+Gk-1TCk-1Gk-1-1,
aˆk=aˆk¯+H¯kTSk-1Yk,
Pk-1=Pk¯-1+H¯kTSk-1H¯k.
P0-1  Λ-1,
a¯0  Λ-1X¯0.
ρf  h1*f1+h2*f1f1,
Q=4I¯1I¯2σI1σI2I¯12+I¯22σI12+σI22,

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