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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 5 — May. 1, 1969
  • pp: 553–556

Optical Spatial Filtering with the Least Mean-Square-Error Filter

JOSEPH L. HORNER  »View Author Affiliations


JOSA, Vol. 59, Issue 5, pp. 553-556 (1969)
http://dx.doi.org/10.1364/JOSA.59.000553


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Abstract

Experimental studies dealing with the restoration of photographic images by optical spatial-filtering techniques are reported. The spatial filters are of a class incorporating predictions of optimum-filtering theory in the presence of random additive noise. This theory was derived using the criterion of least-mean-square error. Measured-modulation-transfer-function curves of both filtered and unfiltered scenes are presented, as well as restorations of continuous tone and binary (Sayce) images distorted by linear motion during exposure. Results show that this type of filtering is superior to that of the infinite signal-to-noise-ratio spatial filter.

Citation
JOSEPH L. HORNER, "Optical Spatial Filtering with the Least Mean-Square-Error Filter," J. Opt. Soc. Am. 59, 553-556 (1969)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-59-5-553


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References

  1. A. Maréchal and P. Croce, Compt. Rend. 237, 706 (1953).
  2. J. Tsujiuchi, in Progress in Optics II, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1963).
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  6. L. Cutrona, E. Leith, C. Palermo, and L. Porcello, Trans. IRE IT-6, 388 (1960).
  7. Lower-case letters will denote the Fourier transform of the corresponding spatial function that appears in upper-case letters.
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  9. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publ. Co., Reading, Mass., 1963), Ch. 2.
  10. The irradiance pattern of the point-spread function on the recording film (aerial image) is further degraded by nonlinear effects of the photographic emulsion. This is discussed further in Sec. IV.
  11. A. Vander Lugt, Trans. IEEE IT-10, 139 (1964).
  12. Although Kodak gives the same designation (649F) to both the plate and film material, the film speed of these two differs by a factor of about 5. Therefore, it is not so surprising that the adjacency effect we measured also differs.
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