This paper focuses on the sufficient condition of block sparse recovery with the -minimization. We show that if the measurement matrix satisfies the block restricted isometry property with , then every block s-sparse signal can be exactly recovered via the -minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013).
This paper first discusses the relationship between the rank null space property (NSP) and the nuclear norm minimization. Several versions of the rank NSP, i.e. the stable rank NSP, robust rank NSP and Frobenius robust rank NSP are proposed, and their equivalent forms are derived. At the same time, it is shown that the stable rank NSP is weaker than the rank restricted isometry property (RIP) to recover the low-rank matrices via the nuclear norm minimization. Finally, the rank NSP is extended to the case of Schatten-[Formula: see text] NSP for [Formula: see text], and the solutions to the Schatten-[Formula: see text] quasi-norm minimization are characterized by the different types of Schatten-[Formula: see text] NSP.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.