The matrix completion method for phase retrieval from fractional Fourier transform magnitudes
type: Item
instance of: scholarly article
title: The matrix completion method for phase retrieval from fractional Fourier transform magnitudes
zbMATH Open document ID: 1400.94059
DOI: 10.1155/2016/4617327
author: Qi Luo
author: Hongxia Wang
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Inspired by the implementation of the fractional Fourier transform (FRFT) and its applications in optics, we address the problem of reconstructing a signal from its several FRFT magnitudes (or intensities). The matrix completion method is adopted here. Through numerical tests, the matrix completion method is proven effective in both noisy and noise-free situations. We also compare our method with the Gerchberg-Saxton (GS) algorithm based on FRFT. Numerical tests show that the matrix completion method gains a certain advantage in recovering uniqueness and convergence over the GS algorithm in the noise-free case. Furthermore, in terms of noisy signals, the matrix completion method performs robustly and adding more measurements can generally increase accuracy of recovered signals.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94A11
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 6953212
Wikidata QID: Q59131350
describes a project that uses: PhaseLift
describes a project that uses: TFOCS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4617327
OpenAlex ID: W2556220857
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description: scientific article; zbMATH DE number 6953212