Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements
The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/959403 |
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| _version_ | 1832561294967832576 |
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| author | Qingshan You Qun Wan Haiwen Xu |
| author_facet | Qingshan You Qun Wan Haiwen Xu |
| author_sort | Qingshan You |
| collection | DOAJ |
| description | The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP_RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming. |
| format | Article |
| id | doaj-art-85047abaacf34228ab23cffb0adf2971 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-85047abaacf34228ab23cffb0adf29712025-02-03T01:25:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/959403959403Restricted Isometry Property of Principal Component Pursuit with Reduced Linear MeasurementsQingshan You0Qun Wan1Haiwen Xu2School of Computer Science, Civil Aviation Flight University of China, GuangHan, Sichuan 618307, ChinaSchool of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Computer Science, Civil Aviation Flight University of China, GuangHan, Sichuan 618307, ChinaThe principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP_RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming.http://dx.doi.org/10.1155/2013/959403 |
| spellingShingle | Qingshan You Qun Wan Haiwen Xu Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements Journal of Applied Mathematics |
| title | Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements |
| title_full | Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements |
| title_fullStr | Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements |
| title_full_unstemmed | Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements |
| title_short | Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements |
| title_sort | restricted isometry property of principal component pursuit with reduced linear measurements |
| url | http://dx.doi.org/10.1155/2013/959403 |
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