Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Recovery from Rank-One Projection Measurements via Nonconvex
  Minimization   In this paper, we consider the matrix recovery from rank-one projection
measurements proposed in [Cai and Zhang, Ann. Statist., 43(2015), 102-138], via
nonconvex minimization. We establish a sufficient identifiability condition,
which can guarantee the exact recovery of low-rank matrix via Schatten-$p$
minimization $\min_{X}\|X\|_{S_p}^p$ for $0<p<1$ under affine constraint, and
stable recovery of low-rank matrix under $\ell_q$ constraint and Dantzig
selector constraint. Our condition is also sufficient to guarantee low-rank
matrix recovery via least $q$ minimization $\min_{X}\|\mathcal{A}(X)-b\|_{q}^q$
for $0<q\leq1$. And we also extend our result to Gaussian design distribution,
and show that any matrix can be stably recovered for rank-one projection from
Gaussian distributions via least $1$ minimization with high probability.

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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th