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Numerical Algebra, Control and Optimization (NACO)
 

Partial $S$-goodness for partially sparse signal recovery

Pages: 25 - 38, Volume 4, Issue 1, March 2014      doi:10.3934/naco.2014.4.25

 
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Lingchen Kong - Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China (email)
Naihua Xiu - Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China (email)
Guokai Liu - Department of Anesthesia, Dongzhimen Hospital, Beijing University of Chinese Medicine, No.5 Haiyuncang, Dongcheng District, Beijing 100700, China (email)

Abstract: In this paper, we will consider the problem of partially sparse signal recovery (PSSR), which is the signal recovery from a certain number of linear measurements when its part is known to be sparse. We establish and characterize partial $s$-goodness for a sensing matrix in PSSR. We show that the partial $s$-goodness condition is equivalent to the partial null space property (NSP), and is weaker than partial restricted isometry property. Moreover, this provides a verifiable approach for partial NSP via partial $s$-goodness constants. We also give exact and stable partially $s$-sparse recovery via the partial $l_1$-norm minimization under mild assumptions.

Keywords:  Partially sparse signal recovery, partial $s$-goodness, partial null space property, exact and stable recovery.
Mathematics Subject Classification:  Primary: 90C26, 65J22; Secondary: 65K10.

Received: May 2013;      Revised: October 2013;      Available Online: December 2013.

 References