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On the Null Space Property oflq-Minimization for0<q≤1in Compressed Sensing

2015; Hindawi Publishing Corporation; Volume: 2015; Linguagem: Inglês

10.1155/2015/579853

2314-8896

Yi Gao, Jigen Peng, Shigang Yue, Yuan Zhao,

Microwave Imaging and Scattering Analysis

The paper discusses the relationship between the null space property (NSP) and the l q -minimization in compressed sensing. Several versions of the null space property, that is, the l q stable NSP, the l q robust NSP, and the l q , p robust NSP for 0 < p ≤ q < 1 based on the standard l q NSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for the l q -minimization can be derived easily under the NSP condition and its equivalent form. Finally, the l q NSP is extended to the l q -synthesis modeling and the mixed l 2 / l q -minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively.