Performance Guarantees for Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices
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We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for ℓ_p quasi-norm minimization generalize to Schatten-p quasi-norm minimization. Based on this theorem, we provide a few RIP-based recovery conditions.
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