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

Lingchen Kong () and Naihua Xiu ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2013, vol. 30, issue 03, 1-13

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}

Keywords: Low-rank matrix recovery; nonconvex Schatten p-minimization; RIP condition (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0217595913400101

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