Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via
  Thresholded Wirtinger Flow   This paper considers the noisy sparse phase retrieval problem: recovering a
sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j =
(a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential
noise $\epsilon_j$. The goals are to understand the effect of the sparsity of
$x$ on the estimation precision and to construct a computationally feasible
estimator to achieve the optimal rates. Inspired by the Wirtinger Flow [12]
proposed for noiseless and non-sparse phase retrieval, a novel thresholded
gradient descent algorithm is proposed and it is shown to adaptively achieve
the minimax optimal rates of convergence over a wide range of sparsity levels
when the $a_j$'s are independent standard Gaussian random vectors, provided
that the sample size is sufficiently large compared to the sparsity of $x$.

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The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an