Modified Gerchberg–Saxton (G-S) Algorithm and Its Application

The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose...
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Autor*in:	Tieyu Zhao [verfasserIn] Yingying Chi [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	G-S algorithm single-phase retrieval algorithm double-phase retrieval algorithm multiple-phase retrieval algorithm image encryption

Übergeordnetes Werk:	In: Entropy - MDPI AG, 2003, 22(2020), 12, p 1354
Übergeordnetes Werk:	volume:22 ; year:2020 ; number:12, p 1354

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/e22121354

Katalog-ID:	DOAJ085513202

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520			\|a The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.
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spelling	10.3390/e22121354 doi (DE-627)DOAJ085513202 (DE-599)DOAJe741c3bbe64f4b9b902e9dfed5ee299b DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Tieyu Zhao verfasserin aut Modified Gerchberg–Saxton (G-S) Algorithm and Its Application 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm. G-S algorithm single-phase retrieval algorithm double-phase retrieval algorithm multiple-phase retrieval algorithm image encryption Science Q Astrophysics Physics Yingying Chi verfasserin aut In Entropy MDPI AG, 2003 22(2020), 12, p 1354 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:22 year:2020 number:12, p 1354 https://doi.org/10.3390/e22121354 kostenfrei https://doaj.org/article/e741c3bbe64f4b9b902e9dfed5ee299b kostenfrei https://www.mdpi.com/1099-4300/22/12/1354 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 22 2020 12, p 1354
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allfieldsSound	10.3390/e22121354 doi (DE-627)DOAJ085513202 (DE-599)DOAJe741c3bbe64f4b9b902e9dfed5ee299b DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Tieyu Zhao verfasserin aut Modified Gerchberg–Saxton (G-S) Algorithm and Its Application 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm. G-S algorithm single-phase retrieval algorithm double-phase retrieval algorithm multiple-phase retrieval algorithm image encryption Science Q Astrophysics Physics Yingying Chi verfasserin aut In Entropy MDPI AG, 2003 22(2020), 12, p 1354 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:22 year:2020 number:12, p 1354 https://doi.org/10.3390/e22121354 kostenfrei https://doaj.org/article/e741c3bbe64f4b9b902e9dfed5ee299b kostenfrei https://www.mdpi.com/1099-4300/22/12/1354 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 22 2020 12, p 1354
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source	In Entropy 22(2020), 12, p 1354 volume:22 year:2020 number:12, p 1354
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authorswithroles_txt_mv	Tieyu Zhao @@aut@@ Yingying Chi @@aut@@
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callnumber-first	Q - Science
author	Tieyu Zhao
spellingShingle	Tieyu Zhao misc QB460-466 misc QC1-999 misc G-S algorithm misc single-phase retrieval algorithm misc double-phase retrieval algorithm misc multiple-phase retrieval algorithm misc image encryption misc Science misc Q misc Astrophysics misc Physics Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
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topic_title	QB460-466 QC1-999 Modified Gerchberg–Saxton (G-S) Algorithm and Its Application G-S algorithm single-phase retrieval algorithm double-phase retrieval algorithm multiple-phase retrieval algorithm image encryption
topic	misc QB460-466 misc QC1-999 misc G-S algorithm misc single-phase retrieval algorithm misc double-phase retrieval algorithm misc multiple-phase retrieval algorithm misc image encryption misc Science misc Q misc Astrophysics misc Physics
topic_unstemmed	misc QB460-466 misc QC1-999 misc G-S algorithm misc single-phase retrieval algorithm misc double-phase retrieval algorithm misc multiple-phase retrieval algorithm misc image encryption misc Science misc Q misc Astrophysics misc Physics
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title	Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
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title_full	Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
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title_sort	modified gerchberg–saxton (g-s) algorithm and its application
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title_auth	Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
abstract	The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.
abstractGer	The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.
abstract_unstemmed	The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which <i<n</i< plaintexts can be recovered from <i<n</i< ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.
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title_short	Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
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Modified Gerchberg–Saxton (G-S) Algorithm and Its Application

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