Sparse Recovery on Euclidean Jordan Algebras
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.
Entry Submitted: 02/03/2013
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