Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

This paper presents a signal and image recovery scheme by the method of alternating projections onto convex sets in optimum fractional Fourier domains. It is shown that the fractional Fourier domain order with minimum bandwidth is the optimum fractional Fourier domain for the method employing altern...

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Published in:Communications in nonlinear science & numerical simulation 2010-03, Vol.15 (3), p.675-689
Main Authors: Serbes, Ahmet, Durak, Lutfiye
Format: Article
Language:English
Subjects:
Fractional Fourier transform
Fractional Fourier transform order estimation
Image recovery
Method of alternating projections
Signal recovery
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description This paper presents a signal and image recovery scheme by the method of alternating projections onto convex sets in optimum fractional Fourier domains. It is shown that the fractional Fourier domain order with minimum bandwidth is the optimum fractional Fourier domain for the method employing alternating projections in signal recovery problems. Following the estimation of optimum fractional Fourier transform orders, incomplete signal is projected onto different convex sets consecutively to restore the missing part. Using a priori information in optimum fractional Fourier domains, superior results are obtained compared to the conventional Fourier domain restoration. The algorithm is tested on 1-D linear frequency modulated signals, real biological data and 2-D signals presenting chirp-type characteristics. Better results are obtained in the matched fractional Fourier domain, compared to not only the conventional Fourier domain restoration, but also other fractional Fourier domains.
doi_str_mv 10.1016/j.cnsns.2009.05.013
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subjects Fractional Fourier transform
Fractional Fourier transform order estimation
Image recovery
Method of alternating projections
Signal recovery
title Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains
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