New Restricted Isometry Condition Using Null Space Constant for Compressed Sensing

摘要

It has been widely recognized that in compressed sensing,many restricted isometry property (RIP) conditions can be easily obtainedby using the null space property (NSP) with its null space constant (NSC)0 < θ ≤ 1 to construct a contradicted method for sparse signal recovery.However, the traditional NSP with θ = 1 will lead to conservative RIP conditions.In this paper, we extend the NSP with 0 < θ < 1 to a scale NSP,which uses a factor to scale down all vectors belonged to the Null spaceof a sensing matrix. Following the popular proof procedure and using thescale NSP, we establish more relaxed RIP conditions with the scale factor , which guarantee the bounded approximation recovery of all sparsesignals in the bounded noisy through the constrained ?_1 minimization. Anapplication verifies the advantages of the scale factor in the number of measurements.