Abstract

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 $O(N^2)$ 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

Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains

M. Fatih Erden and Haldun M. Ozaktas
J. Opt. Soc. Am. A 15(6) 1647-1657 (1998)

Fractional Fourier transforms and imaging

Luís M. Bernardo and Olivério D. D. Soares
J. Opt. Soc. Am. A 11(10) 2622-2626 (1994)

Nonseparable two-dimensional fractional Fourier transform

Aysegul Sahin, M. Alper Kutay, and Haldun M. Ozaktas
Appl. Opt. 37(23) 5444-5453 (1998)

Beam shaping in the fractional Fourier transform domain

Yan Zhang, Bi-Zhen Dong, Ben-Yuan Gu, and Guo-Zhen Yang
J. Opt. Soc. Am. A 15(5) 1114-1120 (1998)

Image rotation, Wigner rotation, and the fractional Fourier transform

Adolf W. Lohmann
J. Opt. Soc. Am. A 10(10) 2181-2186 (1993)