On the Null Space Property of lq-Minimization for 0

Abstract EN

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 NSPfor 0

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.