OPTIMAL IMAGE-RESTORATION WITH THE FRACTIONAL FOURIER-TRANSFORM

The classical Wiener filter, which can be implemented in O(N log N) ti me, is suited best for space-invariant degradation models and space-in variant signal and noise characteristics. For space-varying degradatio ns and nonstationary processes, however, the optimal linear estimate r equires O(N-2) time for implementation. Optimal filtering in fractiona l Fourier domains permits reduction of the error compared with ordinar y 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 w ell as on the degradation model. The largest improvements are typicall y obtained for chirplike degradations and noise, but other types of de gradation and noise may also benefit substantially from the method (e. g., nonconstant velocity motion blur and degradation by inhomogeneous atmospheric turbulence). In any event, these reductions are achieved a t no additional cost. (C) 1998 Optical Society of America.