Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Region-of-Interest reconstruction from truncated cone-beam projections   Region-of-Interest (ROI) tomography aims at reconstructing a region of
interest $C$ inside a body using only x-ray projections intersecting $C$ with
the goal to reduce overall radiation exposure when only a small specific region
of the body needs to be examined. We consider x-ray acquisition from sources
located on a smooth curve $\Gamma$ in $\mathbb{R}^3$ verifying classical Tuy's
condition. In this situation, the {\it non-trucated} cone-beam transform $D f$
of smooth densities $f$ admits an explicit inverse $Z$; however $Z$ cannot
directly reconstruct $f$ from ROI-truncated projections. To deal with the ROI
tomography problem, we introduce a novel reconstruction approach. For densities
$f$ in $L^{\infty}(B)$ where $B$ is a bounded ball in $\mathbb{R}^3$, our
method iterates an operator $U$ combining ROI-truncated projections, inversion
by the operator $Z$ and appropriate regularization operators. Assuming only
knowledge of projections corresponding to a spherical ROI $C \subset B$, given
$\epsilon >0$, we prove that if $C$ is sufficiently large our iterative
reconstruction algorithm converges uniformly to an $\epsilon$-accurate
approximation of $f$, where the accuracy depends on the regularity of $f$
quantified in the Sobolev norm $W^5(B)$. This result shows the existence of a
critical ROI radius ensuring the convergence of the ROI reconstruction
algorithm to $\epsilon$-accurate approximations of $f$. We numerically verified
these theoretical results using simulated acquisition of ROI-truncated
cone-beam projection data for multiple acquisition geometries. Numerical
experiments indicate that the critical ROI radius is fairly small with respect
to the support region~$B$.

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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg