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Partial $S$-goodness for partially sparse signal recovery

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


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