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A Weak Selection Stochastic Gradient Matching Pursuit Algorithm

In the existing stochastic gradient matching pursuit algorithm, the preliminary atomic set includes atoms that do not fully match the original signal. This weakens the reconstruction capability and increases the computational complexity. To solve these two problems, a new method is proposed. Firstly...

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Detalles Bibliográficos
Autores principales: Zhao, Liquan, Hu, Yunfeng, Jia, Yanfei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566407/
https://www.ncbi.nlm.nih.gov/pubmed/31117279
http://dx.doi.org/10.3390/s19102343
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author Zhao, Liquan
Hu, Yunfeng
Jia, Yanfei
author_facet Zhao, Liquan
Hu, Yunfeng
Jia, Yanfei
author_sort Zhao, Liquan
collection PubMed
description In the existing stochastic gradient matching pursuit algorithm, the preliminary atomic set includes atoms that do not fully match the original signal. This weakens the reconstruction capability and increases the computational complexity. To solve these two problems, a new method is proposed. Firstly, a weak selection threshold method is proposed to select the atoms that best match the original signal. If the absolute gradient coefficients were greater than the product of the maximum absolute gradient coefficient and the threshold that was set according to the experiments, then we selected the atoms that corresponded to the absolute gradient coefficients as the preliminary atoms. Secondly, if the scale of the current candidate atomic set was equal to the previous support atomic set, then the loop was exited; otherwise, the loop was continued. Finally, before the transition estimation of the original signal was calculated, we determined whether the number of columns of the candidate atomic set was smaller than the number of rows of the measurement matrix. If this condition was satisfied, then the current candidate atomic set could be regarded as the support atomic set and the loop was continued; otherwise, the loop was exited. The simulation results showed that the proposed method has better reconstruction performance than the stochastic gradient algorithms when the original signals were a one-dimensional sparse signal, a two-dimensional image signal, and a low-rank matrix signal.
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spelling pubmed-65664072019-06-17 A Weak Selection Stochastic Gradient Matching Pursuit Algorithm Zhao, Liquan Hu, Yunfeng Jia, Yanfei Sensors (Basel) Article In the existing stochastic gradient matching pursuit algorithm, the preliminary atomic set includes atoms that do not fully match the original signal. This weakens the reconstruction capability and increases the computational complexity. To solve these two problems, a new method is proposed. Firstly, a weak selection threshold method is proposed to select the atoms that best match the original signal. If the absolute gradient coefficients were greater than the product of the maximum absolute gradient coefficient and the threshold that was set according to the experiments, then we selected the atoms that corresponded to the absolute gradient coefficients as the preliminary atoms. Secondly, if the scale of the current candidate atomic set was equal to the previous support atomic set, then the loop was exited; otherwise, the loop was continued. Finally, before the transition estimation of the original signal was calculated, we determined whether the number of columns of the candidate atomic set was smaller than the number of rows of the measurement matrix. If this condition was satisfied, then the current candidate atomic set could be regarded as the support atomic set and the loop was continued; otherwise, the loop was exited. The simulation results showed that the proposed method has better reconstruction performance than the stochastic gradient algorithms when the original signals were a one-dimensional sparse signal, a two-dimensional image signal, and a low-rank matrix signal. MDPI 2019-05-21 /pmc/articles/PMC6566407/ /pubmed/31117279 http://dx.doi.org/10.3390/s19102343 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Zhao, Liquan
Hu, Yunfeng
Jia, Yanfei
A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title_full A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title_fullStr A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title_full_unstemmed A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title_short A Weak Selection Stochastic Gradient Matching Pursuit Algorithm
title_sort weak selection stochastic gradient matching pursuit algorithm
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566407/
https://www.ncbi.nlm.nih.gov/pubmed/31117279
http://dx.doi.org/10.3390/s19102343
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