Abstract

Three image restoration methods are compared in a variety of blur and noise conditions. Both numerical and subjective data are evaluated. It is demonstrated that, in certain conditions, one restoration method is preferable to others.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. R. Hunt, Proc. IEEE 63, 693 (1975).
    [CrossRef]
  2. M. Cannon, IEEE Trans. Acoust. Speech Signal Proc. ASP-24, 58 (1976).
    [CrossRef]
  3. B. R. Hunt, IEEE Trans. Comput. COM-26, 219 (1977).
    [CrossRef]
  4. T. S. Huang, “Some Notes on Film Grain Noise,” NASA Summer Study on Atmospheric Degradations, Woods Hole, Mass (1968), Appendix, p. 14.
  5. P. D. Welch, IEEE Trans. Audio Electroacoust. AE-15, 70 (1967).
    [CrossRef]
  6. H. J. Trussell, “Improved Methods of Maximum A Posteriori Image Restoration,” Los Alamos Scientific Laboratory Report LA-6516-T (October1976).
  7. B. R. Hunt, T. M. Cannon, IEEE Trans. Systems, Man. Cybern. SMC-6, 876 (1976).
  8. T. Woodlief, Ed., SPSE Handbook of Photographic Science and Engineering (Wiley, New York, 1973).
  9. H. W. Walker, J. Lev, Statistical Inference (Holt, Rinehart and Winston, New York, 1953).
    [CrossRef]

1977

B. R. Hunt, IEEE Trans. Comput. COM-26, 219 (1977).
[CrossRef]

1976

M. Cannon, IEEE Trans. Acoust. Speech Signal Proc. ASP-24, 58 (1976).
[CrossRef]

B. R. Hunt, T. M. Cannon, IEEE Trans. Systems, Man. Cybern. SMC-6, 876 (1976).

1975

B. R. Hunt, Proc. IEEE 63, 693 (1975).
[CrossRef]

1967

P. D. Welch, IEEE Trans. Audio Electroacoust. AE-15, 70 (1967).
[CrossRef]

Cannon, M.

M. Cannon, IEEE Trans. Acoust. Speech Signal Proc. ASP-24, 58 (1976).
[CrossRef]

Cannon, T. M.

B. R. Hunt, T. M. Cannon, IEEE Trans. Systems, Man. Cybern. SMC-6, 876 (1976).

Huang, T. S.

T. S. Huang, “Some Notes on Film Grain Noise,” NASA Summer Study on Atmospheric Degradations, Woods Hole, Mass (1968), Appendix, p. 14.

Hunt, B. R.

B. R. Hunt, IEEE Trans. Comput. COM-26, 219 (1977).
[CrossRef]

B. R. Hunt, T. M. Cannon, IEEE Trans. Systems, Man. Cybern. SMC-6, 876 (1976).

B. R. Hunt, Proc. IEEE 63, 693 (1975).
[CrossRef]

Lev, J.

H. W. Walker, J. Lev, Statistical Inference (Holt, Rinehart and Winston, New York, 1953).
[CrossRef]

Trussell, H. J.

H. J. Trussell, “Improved Methods of Maximum A Posteriori Image Restoration,” Los Alamos Scientific Laboratory Report LA-6516-T (October1976).

Walker, H. W.

H. W. Walker, J. Lev, Statistical Inference (Holt, Rinehart and Winston, New York, 1953).
[CrossRef]

Welch, P. D.

P. D. Welch, IEEE Trans. Audio Electroacoust. AE-15, 70 (1967).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Proc.

M. Cannon, IEEE Trans. Acoust. Speech Signal Proc. ASP-24, 58 (1976).
[CrossRef]

IEEE Trans. Audio Electroacoust.

P. D. Welch, IEEE Trans. Audio Electroacoust. AE-15, 70 (1967).
[CrossRef]

IEEE Trans. Comput.

B. R. Hunt, IEEE Trans. Comput. COM-26, 219 (1977).
[CrossRef]

IEEE Trans. Systems, Man. Cybern.

B. R. Hunt, T. M. Cannon, IEEE Trans. Systems, Man. Cybern. SMC-6, 876 (1976).

Proc. IEEE

B. R. Hunt, Proc. IEEE 63, 693 (1975).
[CrossRef]

Other

T. Woodlief, Ed., SPSE Handbook of Photographic Science and Engineering (Wiley, New York, 1973).

H. W. Walker, J. Lev, Statistical Inference (Holt, Rinehart and Winston, New York, 1953).
[CrossRef]

T. S. Huang, “Some Notes on Film Grain Noise,” NASA Summer Study on Atmospheric Degradations, Woods Hole, Mass (1968), Appendix, p. 14.

H. J. Trussell, “Improved Methods of Maximum A Posteriori Image Restoration,” Los Alamos Scientific Laboratory Report LA-6516-T (October1976).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

The above two 12-bit 480 × 480 images were degraded and used in the image restoration comparison experiment. These and all images used in the experiment were displayed as 6-bit 480 × 480 images on a calibrated COMTAL display system. The images were photographed using Polaroid type 107 film and presented to viewers as 6.5-cm square pictures.

Fig. 2
Fig. 2

The above chart represents one of four families of blurred images that were created for the restoration comparison experiment. Two undegraded images were used as well as two types of blur, which resulted in four such families. Three degrees of blur and noise severity produced nine grandchildren of the original. These nine images were then restored using each of the three methods outlined in the paper. In the case of the bar chart image, the focus blur was applied using a real camera and Kodak 3414 film. There was, therefore, only one level of noise, namely, 3414 scanned with a 10-μm aperture, which corresponds approximately to N3.

Fig. 3
Fig. 3

The above data represent the rankings by twenty-eight observers of the restorations of the blurred images described in Fig. 2. The ordinate represents relative quality, and it can be seen that each restoration method produced an improvement over the original blurred image. In the case of the Gaussian PSF, this improvement is about the same for all three restoration methods. In the case of the focus blur, however, the MAP method appears better able to cope with the singularities and phase reversals present therein. Note that the complete data in Table II can be used to construct graphs such as those above.

Tables (3)

Tables Icon

Table I Mean Square Errors in Intensity

Tables Icon

Table II Mean Square Errors in Density

Tables Icon

Table III Interval Scale Data (Normalized)

Equations (8)

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

g ( x , y ) = s { ϕ [ f ( x , y ) ] } n ( x , y ) ,
g ( x , y ) = s [ h ( x x 1 , y y 1 ) f ( x 1 , y 1 ) d x 1 d y 1 ] + n ( x , y ) ,
g ( x , y ) = h ( x x 1 , y y 1 ) f ( x 1 , y 1 ) d x 1 d y 1 + n ( x , y ) .
D r = D s + ( a g A p ) 1 / 2 D s 1 / 3 n ,
σ n = ( a g A p ) 1 / 2 = ( 0.1446 μ m 2 100 μ m 2 ) 1 / 2 = 0.038.
F w ( u , υ ) = Φ f ( u , υ ) H * ( u , υ ) Φ f ( u , υ ) | H ( u , υ ) | 2 + Φ n ( u , υ ) ,
| F p ( u , υ ) | = [ Φ f ( u , υ ) Φ f ( u , υ ) | H ( u , υ ) | 2 + Φ n ( u , υ ) ] 1 / 2 , F p ( u , υ ) = H ( u , υ ) .
p ( f | g ) = p ( g | f ) p ( f ) p ( g ) .

Metrics