Partial $S$-goodness for partially  sparse signal recovery

Lingchen Kong; Naihua Xiu; Guokai Liu

doi:10.3934/naco.2014.4.25

Article Contents

2014, Volume 4, Issue 1: 25-38. Doi: 10.3934/naco.2014.4.25

This issue Previous Article The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions Next Article Some useful inequalities via trace function method in Euclidean Jordan algebras

Partial $S$-goodness for partially sparse signal recovery

1.
Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044
2.
Department of Anesthesia, Dongzhimen Hospital, Beijing University of Chinese Medicine, No.5 Haiyuncang, Dongcheng District, Beijing 100700

Received: May 2013

Revised: October 2013

Published: November 2013

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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.

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Mathematics Subject Classification: Primary: 90C26, 65J22; Secondary: 65K10.

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