On the null space property of lq -minimization for 0<q≤1 in compressed sensing

Gao, Yi and Peng, Jigen and Yue, Shigang and Zhao, Yuan (2015) On the null space property of lq -minimization for 0<q≤1 in compressed sensing. Journal of Function Spaces, 2015 . p. 579853. ISSN 2314-8896

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On the null space property of lq -minimization for 0<q≤1 in compressed sensing
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Abstract

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. © 2015 Yi Gao et al

Additional Information:This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Journal Title History Journal of Function Spaces 2014–Current Journal of Function Spaces and Applications 2003–2013 (Title Changed) (ISSN 2090-8997, eISSN 0972-6802)
Keywords:Null space property, NSP, Compressed sensing, sparse signals, bmjgoldcheck, NotOAChecked
Subjects:G Mathematical and Computer Sciences > G400 Computer Science
Divisions:College of Science > School of Computer Science
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ID Code:17374
Deposited On:06 May 2015 14:44

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