Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of reconstruction from discrete Radon transform data in
  $\mathbb R^3$ when the function has jump discontinuities   In this paper we study reconstruction of a function $f$ from its discrete
Radon transform data in $\mathbb R^3$ when $f$ has jump discontinuities.
Consider a conventional parametrization of the Radon data in terms of the
affine and angular variables. The step-size along the affine variable is
$\epsilon$, and the density of measured directions on the unit sphere is
$O(\epsilon^2)$. Let $f_\epsilon$ denote the result of reconstruction from the
discrete data. Pick any generic point $x_0$ (i.e., satisfying some mild
conditions), where $f$ has a jump. Our first result is an explicit leading term
behavior of $f_{\epsilon}$ in an $O(\epsilon)$-neighborhood of $x_0$ as
$\epsilon\to0$.
  A closely related question is why can we accurately reconstruct functions
with discontinuities at all? This is a fundamental question, which has not been
studied in the literature in dimensions three and higher. We prove that the
discrete inversion formula `works', i.e. if $x_0\not\in S:=\text{singsupp}(f)$
is generic, then $f_{\epsilon}(x_0)\to f(x_0)$ as $\epsilon\to0$. The proof of
this result reveals a surprising connection with the theory of uniform
distribution (u.d.). This is a new phenomenon that has not been known
previously. We also present some numerical experiments, which confirm the
validity of the developed theory.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg