Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Complex Quadratic Systems with Full-Rank Random Matrices   We tackle the problem of recovering a complex signal $\boldsymbol
x\in\mathbb{C}^n$ from quadratic measurements of the form $y_i=\boldsymbol
x^*\boldsymbol A_i\boldsymbol x$, where $\boldsymbol A_i$ is a full-rank,
complex random measurement matrix whose entries are generated from a
rotation-invariant sub-Gaussian distribution. We formulate it as the
minimization of a nonconvex loss. This problem is related to the well
understood phase retrieval problem where the measurement matrix is a rank-1
positive semidefinite matrix. Here we study the general full-rank case which
models a number of key applications such as molecular geometry recovery from
distance distributions and compound measurements in phaseless diffractive
imaging. Most prior works either address the rank-1 case or focus on real
measurements. The several papers that address the full-rank complex case adopt
the computationally-demanding semidefinite relaxation approach. In this paper
we prove that the general class of problems with rotation-invariant
sub-Gaussian measurement models can be efficiently solved with high probability
via the standard framework comprising a spectral initialization followed by
iterative Wirtinger flow updates on a nonconvex loss. Numerical experiments on
simulated data corroborate our theoretical analysis.

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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc