DocumentCode :
111778
Title :
On the Null Space Constant for {\\ell _p} Minimization
Author :
Laming Chen ; Yuantao Gu
Author_Institution :
Dept. of Electron. Eng., Tsinghua Univ., Beijing, China
Volume :
22
Issue :
10
fYear :
2015
fDate :
Oct. 2015
Firstpage :
1600
Lastpage :
1603
Abstract :
The literature on sparse recovery often adopts the lp “norm” ( p ∈ [0,1]) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding lp minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of lp minimization. In this letter, we show the strict increase of the null space constant in the sparsity level k and its continuity in the exponent p. We also indicate that the constant is strictly increasing in p with probability 1 when the sensing matrix A is randomly generated. Finally, we show how these properties can help in demonstrating the performance of lp minimization, mainly in the relationship between the the exponent p and the sparsity level k.
Keywords :
compressed sensing; computational complexity; minimisation; probability; NP-hardness; lp minimization problem; null space constant; probability; sensing matrix; signal sparse recovery; underdetermined linear system; Materials; Minimization; Null space; Probability distribution; Sensors; Standards; Vectors; ${ell _p}$ minimization; Continuity; monotonicity; null space constant; sparse recovery;
fLanguage :
English
Journal_Title :
Signal Processing Letters, IEEE
Publisher :
ieee
ISSN :
1070-9908
Type :
jour
DOI :
10.1109/LSP.2015.2416003
Filename :
7065209
Link To Document :
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