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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |