Image recovery from double amplitudes in fractional Fourier domain

doi:10.1088/1009-1963/15/2/020

中国物理B ›› 2006, Vol. 15 ›› Issue (2): 347-352.doi: 10.1088/1009-1963/15/2/020

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

Image recovery from double amplitudes in fractional Fourier domain

廖天河, 高穹

Department of Mathematics and Physics, Information and Engineering University, Zhengzhou 450001, China

收稿日期:2005-08-24 修回日期:2005-11-07 出版日期:2006-02-20 发布日期:2006-02-20

Image recovery from double amplitudes in fractional Fourier domain

Liao Tian-He (廖天河), Gao Qiong (高穹)

Department of Mathematics and Physics, Information and Engineering University, Zhengzhou 450001, China

Received:2005-08-24 Revised:2005-11-07 Online:2006-02-20 Published:2006-02-20

摘要/Abstract

摘要： The classical Gerchberg--Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg--Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].

Abstract: The classical Gerchberg--Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg--Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].

Key words: fractional Fourier transform, image recovery, phase retrieval, iterative algorithm

中图分类号: (Phase retrieval)

42.30.Rx

42.30.Va (Image forming and processing) 42.30.Wb (Image reconstruction; tomography) 42.30.Kq (Fourier optics)

廖天河, 高穹. Image recovery from double amplitudes in fractional Fourier domain[J]. 中国物理B, 2006, 15(2): 347-352.

Liao Tian-He (廖天河), Gao Qiong (高穹). Image recovery from double amplitudes in fractional Fourier domain[J]. Chinese Physics, 2006, 15(2): 347-352.

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Image recovery from double amplitudes in fractional Fourier domain

Image recovery from double amplitudes in fractional Fourier domain

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