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Sparse Recovery on Euclidean Jordan Algebras

Lingchen Kong(konglchen***at***126.com)
Jie Sun(jsun***at***nus.edu.sg)
Jiyuan Tao(jtao***at***loyola.edu)
Naihua Xiu(nhxiu***at***bjtu.edu.cn)

Abstract: We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and $s$-goodness for linear transformations in $s$-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions for $s$-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra (NNMEJA). Moreover, we show that both $s$-goodness and NSP are necessary and sufficient conditions for exact $s$-sparse recovery via NNMEJA. Applying the characteristic properties of the proposed conditions, we establish the exact and stable recovery results for SREJA via NNMEJA.

Keywords: Sparse recovery on Euclidean Jordan algebra, nuclear norm minimization, restricted isometry property, null space property, $s$-goodness, exact and stable recovery

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Beijing Jiaotong University, Research report.

Download: [PDF]

Entry Submitted: 02/03/2013
Entry Accepted: 02/03/2013
Entry Last Modified: 02/03/2013

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