Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase retrieval by random binary questions: Which complementary subspace
  is closer?   Phase retrieval in real or complex Hilbert spaces is the task of recovering a
vector, up to an overall unimodular multiplicative constant, from magnitudes of
linear measurements. In this paper, we assume that the vector is normalized,
but retain only qualitative, binary information about the measured magnitudes
by comparing them with a threshold. In more specific, geometric terms, we
choose a sequence of subspaces in a real or complex Hilbert space and only
record whether a given vector is closer to the subspace than to the
complementary subspace. The subspaces have half the dimension of the Hilbert
space and are independent, uniformly distributed with respect to the action of
the orthogonal or unitary groups. The main goal of this paper is to find a
feasible algorithm for approximate recovery based on the information gained
about the vector from these binary questions and to establish error bounds for
its approximate recovery. We provide a pointwise bound for fixed input vectors
and a uniform bound that controls the worst-case scenario among all inputs.
Both bounds hold with high probability with respect to the choice of the
subspaces. For real or complex vectors of dimension $n$, the pointwise bound
requires $m \ge C \delta^{-2} n \log(n)$ and the uniform bound $m \ge C
\delta^{-2} n^2 \log(\delta^{-1} n)$ binary questions in order to achieve an
accuracy of $\delta$. The accuracy $\delta$ is measured by the operator norm of
the difference between the rank-one orthogonal projections corresponding to the
normalized input vector and its approximate recovery.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th