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Journal of Function Spaces
Volume 2015, Article ID 579853, 10 pages
http://dx.doi.org/10.1155/2015/579853
Research Article

On the Null Space Property of -Minimization for in Compressed Sensing

1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
2School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, China
3School of Computer Science, University of Lincoln, Lincoln LN6 7TS, UK

Received 18 December 2014; Revised 1 March 2015; Accepted 2 March 2015

Academic Editor: Yuri Latushkin

Copyright © 2015 Yi Gao et al. 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.

Abstract

The paper discusses the relationship between the null space property (NSP) and the -minimization in compressed sensing. Several versions of the null space property, that is, the stable NSP, the robust NSP, and the robust NSP for based on the standard NSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for the -minimization can be derived easily under the NSP condition and its equivalent form. Finally, the NSP is extended to the -synthesis modeling and the mixed -minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively.