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EXACT LOW-RANK MATRIX RECOVERY VIA NONCONVEX SCHATTEN p-MINIMIZATION

Author

Listed:
  • LINGCHEN KONG

    (Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People's Republic of China)

  • NAIHUA XIU

    (Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People's Republic of China)

Abstract

The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, quantum state tomography, magnetic resonance imaging, system identification and control, and it is generally NP-hard. Recently, Majumdar and Ward [Majumdar, A and RK Ward (2011). An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magnetic Resonance Imaging, 29, 408–417]. had successfully applied nonconvex Schatten p-minimization relaxation of LMR in magnetic resonance imaging. In this paper, our main aim is to establish RIP theoretical result for exact LMR via nonconvex Schatten p-minimization. Carefully speaking, letting $\mathcal{A}$ be a linear transformation from ℝm×n into ℝs and r be the rank of recovered matrix X ∈ ℝm×n, and if $\mathcal{A}$ satisfies the RIP condition $\sqrt{2}\delta_{\max\{r+\lceil\frac{3}{2}k\rceil, 2k\}}+{(\frac{k}{2r})}^{\frac{1}{p}-\frac{1}{2}}\delta_{2r+k}

Suggested Citation

  • Lingchen Kong & Naihua Xiu, 2013. "EXACT LOW-RANK MATRIX RECOVERY VIA NONCONVEX SCHATTEN p-MINIMIZATION," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-13.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:03:n:s0217595913400101
    DOI: 10.1142/S0217595913400101
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    Citations

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    Cited by:

    1. Le Han & Shujun Bi & Shaohua Pan, 2016. "Two-stage convex relaxation approach to least squares loss constrained low-rank plus sparsity optimization problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 119-148, May.
    2. Yu-Fan Li & Kun Shang & Zheng-Hai Huang, 2019. "A singular value p-shrinkage thresholding algorithm for low rank matrix recovery," Computational Optimization and Applications, Springer, vol. 73(2), pages 453-476, June.
    3. Zhaosong Lu & Yong Zhang & Jian Lu, 2017. "$$\ell _p$$ ℓ p Regularized low-rank approximation via iterative reweighted singular value minimization," Computational Optimization and Applications, Springer, vol. 68(3), pages 619-642, December.
    4. Le Han & Shujun Bi, 2018. "Two-stage convex relaxation approach to low-rank and sparsity regularized least squares loss," Journal of Global Optimization, Springer, vol. 70(1), pages 71-97, January.

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