Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase retrieval for characteristic functions of convex bodies and
  reconstruction from covariograms   We propose strongly consistent algorithms for reconstructing the
characteristic function 1_K of an unknown convex body K in R^n from possibly
noisy measurements of the modulus of its Fourier transform \hat{1_K}. This
represents a complete theoretical solution to the Phase Retrieval Problem for
characteristic functions of convex bodies. The approach is via the closely
related problem of reconstructing K from noisy measurements of its covariogram,
the function giving the volume of the intersection of K with its translates. In
the many known situations in which the covariogram determines a convex body, up
to reflection in the origin and when the position of the body is fixed, our
algorithms use O(k^n) noisy covariogram measurements to construct a convex
polytope P_k that approximates K or its reflection -K in the origin. (By recent
uniqueness results, this applies to all planar convex bodies, all
three-dimensional convex polytopes, and all symmetric and most (in the sense of
Baire category) arbitrary convex bodies in all dimensions.) Two methods are
provided, and both are shown to be strongly consistent, in the sense that,
almost surely, the minimum of the Hausdorff distance between P_k and K or -K
tends to zero as k tends to infinity.

21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph