Recovery of low-rank matrices based on the rank null space properties

摘要

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-q NSP for 0 < q < 1, and the solutions to the Schatten-q quasi-norm minimization are characterized by the different types of Schatten-q NSP.