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Stable recovery of low-rank matrix via nonconvex Schatten p-minimization

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Abstract

In this paper, a sufficient condition is obtained to ensure the stable recovery (ɛ ≠ 0) or exact recovery (ɛ = 0) of all r-rank matrices X ∈ ℝm×n from \(b = \mathcal{A}(X) + z\) via nonconvex Schatten p-minimization for any \(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\). Moreover, we determine the range of parameter p with any given δ\(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\). In fact, for any given \(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\), p ∈ (0, 2(1 − δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    WenGu Chen

  2. Graduate School, China Academy of Engineering Physics, Beijing, 100088, China

    YaLing Li

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  1. WenGu Chen
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  2. YaLing Li
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Correspondence to WenGu Chen.

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Chen, W., Li, Y. Stable recovery of low-rank matrix via nonconvex Schatten p-minimization. Sci. China Math. 58, 2643–2654 (2015). https://doi.org/10.1007/s11425-015-5081-6

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  • DOI: https://doi.org/10.1007/s11425-015-5081-6

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