On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing
The paper discusses the relationship between the null space property (NSP) and the lq-minimization in compressed sensing. Several versions of the null space property, that is, the lq stable NSP, the lq robust NSP, and the lq,p robust NSP for 0<p≤q<1 based on the standard lq NSP, are proposed,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/579853 |
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| _version_ | 1832545475623911424 |
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| author | Yi Gao Jigen Peng Shigang Yue Yuan Zhao |
| author_facet | Yi Gao Jigen Peng Shigang Yue Yuan Zhao |
| author_sort | Yi Gao |
| collection | DOAJ |
| description | The paper discusses the relationship between the null space property (NSP) and the lq-minimization in compressed sensing.
Several versions of the null space property, that is, the lq stable NSP, the lq robust NSP, and the lq,p robust NSP
for 0<p≤q<1 based on the standard lq NSP, are proposed, and their equivalent forms are derived.
Consequently, reconstruction results for the lq-minimization can be derived easily under the NSP condition and its equivalent form.
Finally, the lq NSP is extended to the lq-synthesis modeling and the mixed l2/lq-minimization,
which deals with the dictionary-based sparse signals and the block sparse signals, respectively. |
| format | Article |
| id | doaj-art-daf657093ca9482bb53f6ee4d8f78667 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-daf657093ca9482bb53f6ee4d8f786672025-02-03T07:25:50ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/579853579853On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed SensingYi Gao0Jigen Peng1Shigang Yue2Yuan Zhao3School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaSchool of Computer Science, University of Lincoln, Lincoln LN6 7TS, UKSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaThe paper discusses the relationship between the null space property (NSP) and the lq-minimization in compressed sensing. Several versions of the null space property, that is, the lq stable NSP, the lq robust NSP, and the lq,p robust NSP for 0<p≤q<1 based on the standard lq NSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for the lq-minimization can be derived easily under the NSP condition and its equivalent form. Finally, the lq NSP is extended to the lq-synthesis modeling and the mixed l2/lq-minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively.http://dx.doi.org/10.1155/2015/579853 |
| spellingShingle | Yi Gao Jigen Peng Shigang Yue Yuan Zhao On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing Journal of Function Spaces |
| title | On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing |
| title_full | On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing |
| title_fullStr | On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing |
| title_full_unstemmed | On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing |
| title_short | On the Null Space Property of lq-Minimization for 0<q≤1 in Compressed Sensing |
| title_sort | on the null space property of lq minimization for 0 q≤1 in compressed sensing |
| url | http://dx.doi.org/10.1155/2015/579853 |
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