Performance Guarantees for Schatten-p Quasi-Norm Minimization in\n Recovery of Low-Rank Matrices

2014/07/14 by Mohammadreza Malek-Mohammadi, Malek-Mohammadi, Mohammadreza, Massoud Babaie‐Zadeh +3
Engineering · Medicine · Mathematics · #Sparse and Compressive Sensing Techniques #Advanced MRI Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1407.3716

Abstract

We address some theoretical guarantees for Schatten-p quasi-norm\nminimization (p \∈ (0,1]) in recovering low-rank matrices from compressed\nlinear measurements. Firstly, using null space properties of the measurement\noperator, we provide a sufficient condition for exact recovery of low-rank\nmatrices. This condition guarantees unique recovery of matrices of ranks equal\nor larger than what is guaranteed by nuclear norm minimization. Secondly, this\nsufficient condition leads to a theorem proving that all restricted isometry\nproperty (RIP) based sufficient conditions for \ℓ_p quasi-norm minimization\ngeneralize to Schatten-p quasi-norm minimization. Based on this theorem, we\nprovide a few RIP-based recovery conditions.\n

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