A modified iterative algorithm for phase retrieval

Phase retrieval is concerned with the reconstruction of a signal or its Fourier phase from the magnitude of its Fourier transform. In this paper, we address the problem of reconstructing an unknown signal from the following information: the magnitude of the Fourier transform of an unknown signal, a...

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Bibliographic Details
Published in:Journal of the Korean Physical Society Vol. 61; no. 4; pp. 536 - 543
Main Author: Kim, Wooshik
Format: Journal Article
Language:English
Published: Seoul The Korean Physical Society 01.08.2012
한국물리학회
Subjects:
Mathematical and Computational Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Research Papers
Theoretical
물리학
Holographic Interferometry
Phase retrieval
Image reconstruction
ISSN:0374-4884, 1976-8524
Online Access:Get full text
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Summary:Phase retrieval is concerned with the reconstruction of a signal or its Fourier phase from the magnitude of its Fourier transform. In this paper, we address the problem of reconstructing an unknown signal from the following information: the magnitude of the Fourier transform of an unknown signal, a known ‘reference’ signal, and the magnitude of Fourier transform of the signal that is given by the addition of the known reference signal and the unknown desired signal. After we briefly mention an iterative algorithm that is proposed to reconstruct a desired signal from the given information and its convergence properties, we modify the algorithm to improve the convergence property such that the total sum of the squared errors of all the steps composing the algorithm, except the one for imposing magnitude constraints, is non-increasing. Finally, we present some examples that show the properties of convergence against two kinds of noises.
Bibliography:G704-000411.2012.61.4.023
ISSN:0374-4884
1976-8524
DOI:10.3938/jkps.61.536