Sparse Recovery on Euclidean Jordan Algebras

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.