Abstract

The regression analysis for the general image-quality equation (GIQE) [Appl. Opt. 36, 8322–8328 (1997)] was performed using image data from well-corrected optical systems. We conducted human-subject experiments to examine the use of the GIQE with aberrated imagery. A modified image-quality equation for aberrated imagery is presented based on analysis of the experimental results.

© 2010 Optical Society of America

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References

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  1. For a broad, in-depth review of various image-quality metrics see H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).
  2. R. D. Fiete, H. H. Barret, W. E. Smith, and K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945-953 (1987).
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  3. P. G. J. Barten, “Evaluation of subjective image quality with the square-root integral method,” J. Opt. Soc. Am. A 7, 2024-2031 (1990).
    [CrossRef]
  4. J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, and N. Salvaggio, “General image-quality equation: GIQE,” Appl. Opt. 36, 8322-8328 (1997).
    [CrossRef]
  5. J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Systems: Modeling and Performance Prediction (Artech, 2001).
  6. R. D. Fiete and T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
    [CrossRef]
  7. R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
    [CrossRef]
  8. S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
    [CrossRef]
  9. J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).
  10. F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
    [PubMed]
  11. http://www.digitalglobe.com/index.php/86/WorldView-1.
  12. http://www.satimagingcorp.com/satellite-sensors/geoeye-1.html.
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  14. http://www.mathworks.com/products/matlab/.
  15. A. K. Jain, Fundamentals of Digital Image Processing(Prentice Hall, 1989).
  16. N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series (Wiley, 1950).
  17. H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950).
    [CrossRef]
  18. C. W. Helstrom, “Image reconstruction by the method of least squares,” J. Opt. Soc. Am. 57, 297-303 (1967).
    [CrossRef]
  19. S. T. Thurman and J. R. Fienup, “Wiener reconstruction of undersampled imagery,” J. Opt. Soc. Am. A 26, 283-288 (2009).
    [CrossRef]
  20. J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.
  21. P. F. Judy and R. G. Swennsson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
    [CrossRef] [PubMed]
  22. P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163-1176 (1982).
    [CrossRef] [PubMed]
  23. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752-1759 (1985).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[CrossRef]

2002 (1)

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

2001 (1)

R. D. Fiete and T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
[CrossRef]

1999 (1)

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

1997 (1)

1990 (1)

1987 (1)

1985 (1)

1982 (1)

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163-1176 (1982).
[CrossRef] [PubMed]

1981 (1)

P. F. Judy and R. G. Swennsson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

1967 (1)

1966 (1)

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
[PubMed]

1950 (1)

H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950).
[CrossRef]

Barret, H. H.

Barrett, H. H.

Barten, P. G. J.

Bode, H. W.

H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950).
[CrossRef]

Borgstrom, M. C.

Brown, S. D.

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

Calus, J. R.

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

Campbell, F. W.

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
[PubMed]

Colburn, L.

Driggers, R. G.

J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Systems: Modeling and Performance Prediction (Artech, 2001).

Eng, R.

J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.

Fienup, J. R.

S. T. Thurman and J. R. Fienup, “Wiener reconstruction of undersampled imagery,” J. Opt. Soc. Am. A 26, 283-288 (2009).
[CrossRef]

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[CrossRef]

Fiete, R. D.

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

R. D. Fiete and T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
[CrossRef]

R. D. Fiete, H. H. Barret, W. E. Smith, and K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945-953 (1987).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Gross, H. N.

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

Guignard, P. A.

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163-1176 (1982).
[CrossRef] [PubMed]

Hadaway, J. B.

J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.

Helstrom, C. W.

Hogue, B.

J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.

Irvine, J.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing(Prentice Hall, 1989).

Judy, P. F.

P. F. Judy and R. G. Swennsson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

Kulikowski, J. J.

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
[PubMed]

Leachtenauer, J. C.

J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, and N. Salvaggio, “General image-quality equation: GIQE,” Appl. Opt. 36, 8322-8328 (1997).
[CrossRef]

J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Systems: Modeling and Performance Prediction (Artech, 2001).

Levinson, J.

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
[PubMed]

Malila, W.

Mooney, J. A.

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

Myers, K.

For a broad, in-depth review of various image-quality metrics see H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

Myers, K. J.

Patton, D. D.

Raqueno, R. V.

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

Robinson, G.

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

Salvaggio, N.

Schott, J. R.

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

Seeley, G. W.

Shannon, C. E.

H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950).
[CrossRef]

Smith, W. E.

Stahl, P.

J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.

Swennsson, R. G.

P. F. Judy and R. G. Swennsson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

Tantalo, T.

R. D. Fiete and T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
[CrossRef]

Tantalo, T. A.

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

Thurman, S. T.

S. T. Thurman and J. R. Fienup, “Wiener reconstruction of undersampled imagery,” J. Opt. Soc. Am. A 26, 283-288 (2009).
[CrossRef]

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[CrossRef]

Wiener, N.

N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series (Wiley, 1950).

Appl. Opt. (1)

Can. J. Remote Sens. (1)

J. R. Schott, S. D. Brown, R. V. Raqueno, H. N. Gross, and G. Robinson, “An advanced synthetic image generation model and its application to multi/hyperspectral algorithm development,” Can. J. Remote Sens. 25, 99-111 (1999).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Physiol. (1)

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. 187, 427-436 (1966).
[PubMed]

Med. Phys. (1)

P. F. Judy and R. G. Swennsson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

Opt. Eng. (2)

R. D. Fiete and T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
[CrossRef]

R. D. Fiete, T. A. Tantalo, J. R. Calus, and J. A. Mooney, “Image quality of sparse-aperture designs for remote sensing,” Opt. Eng. 41, 1957-1969 (2002).
[CrossRef]

Phys. Med. Biol. (1)

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163-1176 (1982).
[CrossRef] [PubMed]

Proc. IRE (1)

H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950).
[CrossRef]

Proc. SPIE (1)

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[CrossRef]

Other (9)

For a broad, in-depth review of various image-quality metrics see H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Systems: Modeling and Performance Prediction (Artech, 2001).

http://www.digitalglobe.com/index.php/86/WorldView-1.

http://www.satimagingcorp.com/satellite-sensors/geoeye-1.html.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

http://www.mathworks.com/products/matlab/.

A. K. Jain, Fundamentals of Digital Image Processing(Prentice Hall, 1989).

N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series (Wiley, 1950).

J. B. Hadaway, P. Stahl, R. Eng, and B. Hogue, “Cryogenic test results of Hextek mirror,” presented at Mirror Technology Days 2004, Huntsville, Alabama, USA, 17-19 August 2004.

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Figures (10)

Fig. 1
Fig. 1

Digital resolution target used for experiment.

Fig. 2
Fig. 2

Portions of the simulated baseline image (a) before and (b) after postprocessing. The portion shown here corresponds to rows 4–10 of the eye chart with corresponding line widths 1.00, 0.794, 0.630, 0.500, 0.397, 0.315, and 0.250 m (from top to bottom).

Fig. 3
Fig. 3

Portion of simulated reference image corresponding to Δ NIIRS = 0.98 compared to the baseline image shown in Fig. 2(b).

Fig. 4
Fig. 4

Portion of simulated image with 0.5 waves P–V of defocus and SNR = 50 (a) before and (b) after postprocessing.

Fig. 5
Fig. 5

Variation of log 2 ( RER ) , G / SNR , and H with the amount of defocus for SNR = 200 , 50, and 10. The marked points represent the values for the images that were evaluated by human subjects.

Fig. 6
Fig. 6

Observed Δ NIIRS values obtained from human subjects for defocused imagery with SNR = 200 , 50, and 10. The dashed curves represent the modified GIQE, Δ NIIRS = 0.291 + log 2 ( RER ) 2.229 G / SNR , obtained from the analysis in Section 4.

Fig. 7
Fig. 7

Spatial distribution of mid-spatial-frequency aberrations for a segmented primary mirror.

Fig. 8
Fig. 8

Portion of simulated image with 0.15 waves RMS of mid-spatial-frequency aberration and SNR = 50 (a) before and (b) after postprocessing.

Fig. 9
Fig. 9

Variation of log 2 ( RER ) , G / SNR , and H with the amount of mid-spatial-frequency aberration for SNR = 200 , 50, and 10. The marked points represent the values for the images that were evaluated by human subjects.

Fig. 10
Fig. 10

Observed Δ NIIRS values obtained from human subjects for imagery with mid-spatial-frequency aberrations and SNR = 200 , 50, and 10. The dashed curves represent the modified GIQE, Δ NIIRS = 0.283 + log 2 ( RER ) 2.574 G / SNR , obtained from the analysis in Section 4.

Tables (6)

Tables Icon

Table 1 General Image-Quality Equation Coefficient Values [4, 5] a

Tables Icon

Table 2 Statistics of General Image-Quality Equation Terms for Imagery Used to Develop GIQE 4.0 [4]

Tables Icon

Table 3 Simulation Parameters for Baseline Image Shown in Fig. 2

Tables Icon

Table 4 Image-Quality Parameters for Baseline Image

Tables Icon

Table 5 Analysis of Results for Imagery with Defocus Aberration

Tables Icon

Table 6 Analysis of Results for Imagery with Mid-Spatial-Frequency Aberration

Equations (15)

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

NIIRS = c 0 + c 1 log 10 ( GSD ) + c 2 log 10 ( RER ) + c 3 G / SNR + c 4 H ,
GSD = p R / f ,
RER = ER ( 0.5 p ) ER ( 0.5 p ) ,
ER ( x ) = 0 d x d y s ( x x , y ) ,
H = { ER ( 1.25 p ) , when     d ER ( x ) d x 0 for all     x [ 1 p , 3 p ] max { ER ( x ) }   on interval   x [ 1 p , 3 p ] , otherwise .
SNR = N 2 N + σ 2 ,
w = [ 0.2 0.4 0.2 0.4 3.4 0.4 0.2 0.4 0.2 ] .
G = ( m , n ) w m , n 2 ( m , n ) w m , n ,
Δ NIIRS = log 2 ( GSD 0 / GSD ) ,
Φ o ( ρ ) = { A 0 2 for     ρ = 0 A 2 ρ 2 α for     ρ 0 .
Φ n = N + σ 2 ,
A 0 = M N ,
μ e = 1 K k ( Δ NIIRS obs , k Δ NIIRS iqe , k ) ,
σ e 2 = 1 K k ( Δ NIIRS obs , k Δ NIIRS iqe , k ) 2 ,
R 2 = 1 k ( Δ NIIRS obs , k Δ NIIRS iqe , k ) 2 k ( Δ NIIRS obs , k Δ NIIRS obs , avg ) 2 ,

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