Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems
We introduce a novel iterative algorithm, termed the Heavy-Ball-Based Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HBHTP), to reconstruct a sparse signal from a small number of magnitude-only measurements. Our algorithm is obtained via a natural combination of the Hard Threshold...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2744 |
| _version_ | 1797593690851508224 |
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| author | Yingying Li Jinchuan Zhou Zhongfeng Sun Jingyong Tang |
| author_facet | Yingying Li Jinchuan Zhou Zhongfeng Sun Jingyong Tang |
| author_sort | Yingying Li |
| collection | DOAJ |
| description | We introduce a novel iterative algorithm, termed the Heavy-Ball-Based Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HBHTP), to reconstruct a sparse signal from a small number of magnitude-only measurements. Our algorithm is obtained via a natural combination of the Hard Thresholding Pursuit for sparse phase retrieval (SPR-HTP) and the classical Heavy-Ball (HB) acceleration method. The robustness and convergence for the proposed algorithm were established with the help of the restricted isometry property. Furthermore, we prove that our algorithm can exactly recover a sparse signal with overwhelming probability in finite steps whenever the initialization is in the neighborhood of the underlying sparse signal, provided that the measurement is accurate. Extensive numerical tests show that SPR-HBHTP has a markedly improved recovery performance and runtime compared to existing alternatives, such as the Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HTP), the SPARse Truncated Amplitude Flow (SPARTA), and Compressive Phase Retrieval with Alternating Minimization (CoPRAM). |
| first_indexed | 2024-03-11T02:11:59Z |
| format | Article |
| id | doaj.art-fc4804ee91c945ac8f080b351fc0fab1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:11:59Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fc4804ee91c945ac8f080b351fc0fab12023-11-18T11:29:10ZengMDPI AGMathematics2227-73902023-06-011112274410.3390/math11122744Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval ProblemsYingying Li0Jinchuan Zhou1Zhongfeng Sun2Jingyong Tang3School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaSchool of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaSchool of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaSchool of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaWe introduce a novel iterative algorithm, termed the Heavy-Ball-Based Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HBHTP), to reconstruct a sparse signal from a small number of magnitude-only measurements. Our algorithm is obtained via a natural combination of the Hard Thresholding Pursuit for sparse phase retrieval (SPR-HTP) and the classical Heavy-Ball (HB) acceleration method. The robustness and convergence for the proposed algorithm were established with the help of the restricted isometry property. Furthermore, we prove that our algorithm can exactly recover a sparse signal with overwhelming probability in finite steps whenever the initialization is in the neighborhood of the underlying sparse signal, provided that the measurement is accurate. Extensive numerical tests show that SPR-HBHTP has a markedly improved recovery performance and runtime compared to existing alternatives, such as the Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HTP), the SPARse Truncated Amplitude Flow (SPARTA), and Compressive Phase Retrieval with Alternating Minimization (CoPRAM).https://www.mdpi.com/2227-7390/11/12/2744sparse phase retrievalHeavy-Ball methodHard Thresholding Pursuitrestricted isometry property |
| spellingShingle | Yingying Li Jinchuan Zhou Zhongfeng Sun Jingyong Tang Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems Mathematics sparse phase retrieval Heavy-Ball method Hard Thresholding Pursuit restricted isometry property |
| title | Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems |
| title_full | Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems |
| title_fullStr | Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems |
| title_full_unstemmed | Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems |
| title_short | Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems |
| title_sort | heavy ball based hard thresholding pursuit for sparse phase retrieval problems |
| topic | sparse phase retrieval Heavy-Ball method Hard Thresholding Pursuit restricted isometry property |
| url | https://www.mdpi.com/2227-7390/11/12/2744 |
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