Optimal image restoration with the fractional Fourier transform

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage833en_US
dc.citation.issueNumber4en_US
dc.citation.spage825en_US
dc.citation.volumeNumber15en_US
dc.contributor.authorKutay, M. A.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2016-02-08T10:46:09Z
dc.date.available2016-02-08T10:46:09Z
dc.date.issued1998-04en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractThe 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.en_US
dc.identifier.doi10.1364/JOSAA.15.000825en_US
dc.identifier.issn0740-3232
dc.identifier.urihttp://hdl.handle.net/11693/25520
dc.language.isoEnglishen_US
dc.publisherOSA - The Optical Societyen_US
dc.relation.isversionofhttps://doi.org/10.1364/JOSAA.15.000825en_US
dc.source.titleJournal of the Optical Society of America A: Optics and Image Science, and Visionen_US
dc.subjectDifferential equationsen_US
dc.subjectDiffractionen_US
dc.subjectEstimationen_US
dc.subjectFourier opticsen_US
dc.subjectFourier transformsen_US
dc.subjectHolographyen_US
dc.subjectLight propagationen_US
dc.subjectMathematical modelsen_US
dc.subjectOptical systemsen_US
dc.subjectSignal processingen_US
dc.subjectStatistical opticsen_US
dc.subjectWhite noiseen_US
dc.subjectFractional Fourier transformen_US
dc.subjectMean square erroren_US
dc.subjectWiener filteringen_US
dc.subjectImage reconstructionen_US
dc.titleOptimal image restoration with the fractional Fourier transformen_US
dc.typeArticleen_US
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