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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 825–833

Optimal image restoration with the fractional Fourier transform

M. Alper Kutay and Haldun M. Ozaktas  »View Author Affiliations

JOSA A, Vol. 15, Issue 4, pp. 825-833 (1998)

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The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for space-invariant degradation models and space-invariant signal and noise characteristics. For space-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. Optimal filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain Wiener filtering for certain types of degradation and noise while requiring only O(N log N) implementation time. The amount of reduction in error depends on the signal and noise statistics as well as on the degradation model. The largest improvements are typically obtained for chirplike degradations and noise, but other types of degradation and noise may also benefit substantially from the method (e.g., nonconstant velocity motion blur and degradation by inhomegeneous atmospheric turbulence). In any event, these reductions are achieved at no additional cost.

© 1998 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.3020) Image processing : Image reconstruction-restoration

Original Manuscript: August 29, 1997
Revised Manuscript: November 7, 1997
Manuscript Accepted: September 29, 1997
Published: April 1, 1998

M. Alper Kutay and Haldun M. Ozaktas, "Optimal image restoration with the fractional Fourier transform," J. Opt. Soc. Am. A 15, 825-833 (1998)

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