Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Deterministic Theory for Exact Non-Convex Phase Retrieval   In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for
phase retrieval and identify a novel sufficient condition for universal exact
recovery through the lens of low rank matrix recovery theory. Via a perspective
in the lifted domain, we show that the convergence of the WF iterates to a true
solution is attained geometrically under a single condition on the lifted
forward model. As a result, a deterministic relationship between the accuracy
of spectral initialization and the validity of {the regularity condition} is
derived. In particular, we determine that a certain concentration property on
the spectral matrix must hold uniformly with a sufficiently tight constant.
This culminates into a sufficient condition that is equivalent to a restricted
isometry-type property over rank-1, positive semi-definite matrices, and
amounts to a less stringent requirement on the lifted forward model than those
of prominent low-rank-matrix-recovery methods in the literature. We
characterize the performance limits of our framework in terms of the tightness
of the concentration property via novel bounds on the convergence rate and on
the signal-to-noise ratio such that the theoretical guarantees are valid using
the spectral initialization at the proper sample complexity.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th