Abstract

Image-quality criteria are usually intended to achieve the best possible image at a given sampling rate, which is ill-suited to applications where the detection of well-defined geometric and radiometric properties of scenes or objects are paramount. The quality criterion developed here for designing observation systems is based on properties of the objects to be viewed. It is thus an object-oriented imaging quality criterion rather than an image-oriented one. We also propose to go beyond optimization and calibrate a numerical scale that can be used to rate the quality of the service delivered by any observation system.

© 2001 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).
  2. P. Z. Mouroulis, H. Zhang, “Visual instrument image quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
    [CrossRef] [PubMed]
  3. P. Z. Mouroulis, X. Cheng, “Visual instrument image-quality assessment with rotationally symmetric difference of Gaussians,” Appl. Opt. 36, 1667–1670 (1997).
    [CrossRef] [PubMed]
  4. E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photograph. Sci. Eng. 16, 221–230 (1972).
  5. H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision at the National Academy of Sciences, Washington, D.C., 1970.
  6. A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).
  7. P. G. Barten, “Evaluation of subjective image quality with the square-root integral method,” J. Opt. Soc. Am. A 7, 2024–2031 (1990).
    [CrossRef]
  8. A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
    [CrossRef] [PubMed]
  9. F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
    [CrossRef]
  10. S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
    [CrossRef]
  11. C. L. Fales, F. O. Huck, R. W. Samms, “Imaging system design for improved information capacity,” Appl. Opt. 23, 872–888 (1984).
    [CrossRef] [PubMed]
  12. F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
    [CrossRef]
  13. C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” in SID Digest (Society for Information Display, Santa Ana, Calif.1980), Vol. 21/3, pp. 229–246.
  14. A. B. Watson, ed., Digital Images and Human Vision (MIT Press, Cambridge, Mass., 1993).
  15. A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
    [CrossRef]
  16. A. B. Watson, Joshua A. Solomon, “Model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2391 (1997).
    [CrossRef]
  17. A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
    [CrossRef]
  18. PQA300: Picture Quality Analysis System, TEKTRONIX, http://www.tektronix.com/ .
  19. J. Lubin, M. Brill, R. Crane, “Vision model-based assessment of distortion magnitudes in digital video,” http://www.mpeg.org/MPEG/JND .
  20. Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1999).
  21. P. B. Fellget, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 369–407 (1955).
    [CrossRef]
  22. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  23. R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).
  24. C. L. Fales, F. O. Huck, J. A. McCormick, S. K. Park, “Wiener restoration of sampled image data: end-to-end analysis,” J. Opt. Soc. Am. A 5, 300–314 (1988).
    [CrossRef]
  25. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
    [CrossRef] [PubMed]
  26. D. J. Field, “Scale-invariance and self-similar ‘wavelet’ transforms: an analysis of natural scenes and mammalian visual systems,” in Wavelets, Fractals, and Fourier Transforms, M. Farge, J. C. Hunt, J. C. Vassilicos, eds. (Clarendon, Oxford, UK, 1993).
  27. G. J. Burton, I. R. Moorhead, “Color and spatial structure in natural scenes,” Appl. Opt. 26, 157–170 (1987).
    [CrossRef] [PubMed]
  28. D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
    [CrossRef]
  29. STANAG 3769 (about the minimal resolution needed for photographic interpretation), NATO Standardization Agreements (NATO, Brussels, year unknown).
  30. Imagery Resolution Assessments and Reporting (IRARS) Committee, “National imagery interpretability rating scale (NIIRS),” http://www.fas.org/irp/imint/niirs_c/guide.htm .
  31. J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, N. Salvaggio, “General image-quality equation: GIQE,” Appl. Opt. 36, 8322–8328 (1997).
    [CrossRef]
  32. C. L. Fales, F. O. Huck, R. W. Samms, “Imaging system design for improved information capacity,” Appl. Opt. 23, 872–888 (1984).
    [CrossRef] [PubMed]

1999 (2)

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

1997 (3)

1996 (1)

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

1994 (1)

D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
[CrossRef]

1992 (1)

1991 (1)

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
[CrossRef]

1990 (1)

1988 (1)

1987 (2)

1984 (2)

1972 (1)

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photograph. Sci. Eng. 16, 221–230 (1972).

1955 (1)

P. B. Fellget, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 369–407 (1955).
[CrossRef]

Alter-Gartenberg, R.

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
[CrossRef]

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Barten, P. G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Borthwick, R.

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Buck, John R.

Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1999).

Burton, G. J.

Carlson, C. R.

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” in SID Digest (Society for Information Display, Santa Ana, Calif.1980), Vol. 21/3, pp. 229–246.

Cheng, X.

Cohen, R. W.

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” in SID Digest (Society for Information Display, Santa Ana, Calif.1980), Vol. 21/3, pp. 229–246.

Colburn, L.

Cupery, K. N.

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photograph. Sci. Eng. 16, 221–230 (1972).

Fales, C. L.

Fellget, P. B.

P. B. Fellget, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 369–407 (1955).
[CrossRef]

Field, D. J.

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

D. J. Field, “Scale-invariance and self-similar ‘wavelet’ transforms: an analysis of natural scenes and mammalian visual systems,” in Wavelets, Fractals, and Fourier Transforms, M. Farge, J. C. Hunt, J. C. Vassilicos, eds. (Clarendon, Oxford, UK, 1993).

Gonzalez, R. C.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Granger, E. M.

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photograph. Sci. Eng. 16, 221–230 (1972).

Huck, F. O.

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
[CrossRef]

C. L. Fales, F. O. Huck, J. A. McCormick, S. K. Park, “Wiener restoration of sampled image data: end-to-end analysis,” J. Opt. Soc. Am. A 5, 300–314 (1988).
[CrossRef]

C. L. Fales, F. O. Huck, R. W. Samms, “Imaging system design for improved information capacity,” Appl. Opt. 23, 872–888 (1984).
[CrossRef] [PubMed]

C. L. Fales, F. O. Huck, R. W. Samms, “Imaging system design for improved information capacity,” Appl. Opt. 23, 872–888 (1984).
[CrossRef] [PubMed]

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Irvine, J.

Leachtenauer, J. C.

Linfoot, E. H.

P. B. Fellget, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 369–407 (1955).
[CrossRef]

Malila, W.

McCormick, J. A.

Moorhead, I. R.

Mouroulis, P. Z.

Oppenheim, Alan V.

Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1999).

Park, S. K.

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

C. L. Fales, F. O. Huck, J. A. McCormick, S. K. Park, “Wiener restoration of sampled image data: end-to-end analysis,” J. Opt. Soc. Am. A 5, 300–314 (1988).
[CrossRef]

Rahman, Z.

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
[CrossRef]

Ruderman, D. L.

D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
[CrossRef]

Salvaggio, N.

Samms, R. W.

Schafer, Ronald W.

Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1999).

Snyder, H. L.

H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision at the National Academy of Sciences, Washington, D.C., 1970.

Solomon, Joshua A.

Taylor, M.

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

van der Schaaf, A.

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Meeteren, A.

A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).

Watson, A. B.

A. B. Watson, Joshua A. Solomon, “Model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2391 (1997).
[CrossRef]

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
[CrossRef]

Wintz, P.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Zhang, H.

Appl. Opt. (5)

CVGIP Graph. Models Image Process (1)

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” CVGIP Graph. Models Image Process. 53, 71–84 (1991).
[CrossRef]

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

Network (1)

D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
[CrossRef]

Opt. Eng. (2)

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

Philos. Trans. R. Soc. London (1)

P. B. Fellget, E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. London 247, 369–407 (1955).
[CrossRef]

Photograph. Sci. Eng. (1)

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photograph. Sci. Eng. 16, 221–230 (1972).

Vision Res. (1)

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

Other (15)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision at the National Academy of Sciences, Washington, D.C., 1970.

A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” in SID Digest (Society for Information Display, Santa Ana, Calif.1980), Vol. 21/3, pp. 229–246.

A. B. Watson, ed., Digital Images and Human Vision (MIT Press, Cambridge, Mass., 1993).

A. B. Watson, “DCT quantization matrices visually optimized for individual images,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 202–216 (1993).
[CrossRef]

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

PQA300: Picture Quality Analysis System, TEKTRONIX, http://www.tektronix.com/ .

J. Lubin, M. Brill, R. Crane, “Vision model-based assessment of distortion magnitudes in digital video,” http://www.mpeg.org/MPEG/JND .

Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1999).

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

STANAG 3769 (about the minimal resolution needed for photographic interpretation), NATO Standardization Agreements (NATO, Brussels, year unknown).

Imagery Resolution Assessments and Reporting (IRARS) Committee, “National imagery interpretability rating scale (NIIRS),” http://www.fas.org/irp/imint/niirs_c/guide.htm .

D. J. Field, “Scale-invariance and self-similar ‘wavelet’ transforms: an analysis of natural scenes and mammalian visual systems,” in Wavelets, Fractals, and Fourier Transforms, M. Farge, J. C. Hunt, J. C. Vassilicos, eds. (Clarendon, Oxford, UK, 1993).

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Figures (14)

Fig. 1
Fig. 1

Model of image acquisition and reconstruction.

Fig. 2
Fig. 2

Radiometric image of rectangles: model for a four-door car.

Fig. 3
Fig. 3

Example of the “surface-of-difference-area” determination between two rectangles of equal widths.

Fig. 4
Fig. 4

Example of the “surface-of-difference-area” determination between two rectangles of different widths.

Fig. 5
Fig. 5

Comparison between an isolated signal and the same signal stuck to another of equal strength. Here the case LPSF2L is represented.

Fig. 6
Fig. 6

Left to right: five-door car, four-door car. In a five-door car, the trunk gives access to the rest of the car, and its apparent surface (seen from above) is noticeably less than that of the four-door trunk.

Fig. 7
Fig. 7

Left to right: truck, coach, four-door car, and five-door car.

Fig. 8
Fig. 8

Plot of the energy in the fidelity measure calculated with a standard resolution independent of the elongation, by using Eq. (10).

Fig. 9
Fig. 9

Energy plot used in the fidelity measure calculation with a standard resolution given by the model of Eq. (13) and α=0.9.

Fig. 10
Fig. 10

Comparison between the original signal (dashed curve) and the filtered signal (solid curve).

Fig. 11
Fig. 11

Comparison between the original signal (dashed curve) and the filtered and noisy signal (solid curve). The noise part to consider in calculating the modified fidelity measure is circled in gray.

Fig. 12
Fig. 12

Image of a parking lot of vehicles having the same contrast, all others having been deleted.

Fig. 13
Fig. 13

Example of bimodal histogram of the measurement of quality for one image.

Fig. 14
Fig. 14

Averaged measure of viewers versus the modified fidelity criteria for the 54 images of the experiment. The vertical bar above and below the crosses represents one root mean square of the measurement process. The correlation is 0.91.

Tables (1)

Tables Icon

Table 1 Ease of Distinction between the Objects of the List

Equations (29)

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

S(i, j)=K×[L(x, y)*h(x, y)](i×le, j×le)+N(i, j),
LR(x, y)=K×[L(x, y)*(x, y)+NBL(x, y)]×Шxle,xle*sincxle,yle,
fidelity(image, imagereconstructed)=image-imagereconstructedL22imageL22=FT[image]-FT[imagereconstructed]L22FT[Image]L22=1FT[image]L22×|FT[image](νx,νy)-FT[imagereconstructed](νx,νy)|2dνxdνy,
FT[image]L22=C×0ν00ν01(νx2+νy2)α/2dνxdνy+[0,+]2-[0,ν0]21(νx2+νy2)α/2dνxdνy.
 α[0, 2],0ν00ν01(νx2+νy2)α/2dνxdνy+,
 α[2, ],ν0+ν0+1(νx2+νy2)α/2dνxdνy+.
fidelitymission(image, imageconstructed)=[-νmax,νmax]2-[-νmin,νmin]2|FT[image](νx,νy)-FT[imagereconstructed](νx,νy)|2dνxdνy[-νmax,νmax]2-[-νmin,νmin]2|FT[image](νx,νy)|2dνxdνy.
fmax=2×12×resolutionstandard.
0νmax(shape)0νmax(shape)|FT[shape](νx,νy)|2dνxdνy=const.
resolutionstandardsquare=surfacesquare4=surfacesquare2.
νmax(square)=12×1resolutionstandardsquare2=2surfacesquare.
max[Lx, Ly]min[Lx, Ly],
02/surface02/surface×|FT[rectangle(elongation)](νx,νy)|2dνxdνy.
resolutionstandard=min[Lx, Ly]α×max[Lx, Ly]1-α2,
fidelitymission(shape, shapereconstructed)=[-νe/2, νe/2]2|FT[shape]-(i, j)[hˆ×FT[shape]](νx-iνe,νy-jνe)|(νx,νy)2dνxdνy[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy+[-νmax,νmax]2-[-νe/2, νe/2]2|FT[shape](νx,νy)|2dνxdνy+[-νe/2, νe/2]2|NˆBLshape|(νx,νy)2dνxdνy[-νmax,νmax]2|FT[shape](νx,νy)|2dνxdνy.
fidelitymissionfiltering(shape, shapereconstructed)=[-νe/2, νe/2]2|FT[shape]-hˆ×FT[shape]|(νx, νy)2dνxdνy[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy,
fidelitymissionaliasing(shape, shapereconstructed)=1[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy×[-νe/2, νe/2]2(i, j)(0, 0)hˆ×FT[shape](νx-iνe, νy-jνe)2dνxdνy-2×[-νe/2, νe/2]2(i, j)(0, 0)[hˆ×FT[shape]](νx-iνe, νy-jνe)×[(1-hˆ)×FT[shape]](νx, νy)dνxdνy,
fidelitymissionnoise(shape, shapeconstructed)=shape|NBL|(x, y)2dxdy[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy,
fidelitymissionloss(shape, shapereconstructed)=[-νmax,νmax]2-[-νe/2, νe/2]2|FT[shape](νx, νy)|2dνxdνy[-νmax, νmax]2|FT[shape](νx, νy)|2dνxdνy.
fidelitymissionnoise(shape, shapereconstructed)=surface×σn2[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy,
[-νmax,νmax]2|FT[shape](νx, νy)|2dνxdνy
=-2/L2/L-2/L2/Lsinc(νxL)sinc(νyL)dνxdνy
=-2/L2/Lsinc(νL)d2.
-2/L2/Lsinc(νL)dν/-+sinc(νL)dν0.9,
fidelitymissionnoise(shape, shaperecostructed)
=surface×σn20.9×[-,+]2|FT[shape](νx, νy)|2dνxdνy
=surface×σn20.9×[-,+]2|[shape](x, y)|2dxdy
=surface×σn20.9×surface×constrastshape2
=σn20.9×constrastshape2.

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