Exact inversion of the conical Radon transform with a fixed opening angle
R Gouia-Zarrad, G Ambartsoumian - arXiv preprint arXiv:1309.6581, 2013 - arxiv.org
arXiv preprint arXiv:1309.6581, 2013•arxiv.org
We study a new class of Radon transforms defined on circular cones called the conical
Radon transform. In $\mathbb {R}^ 3$ it maps a function to its surface integrals over circular
cones, and in $\mathbb {R}^ 2$ it maps a function to its integrals along two rays with a
common vertex. Such transforms appear in various mathematical models arising in medical
imaging, nuclear industry and homeland security. This paper contains new results about
inversion of conical Radon transform with fixed opening angle and vertical central axis in …
Radon transform. In $\mathbb {R}^ 3$ it maps a function to its surface integrals over circular
cones, and in $\mathbb {R}^ 2$ it maps a function to its integrals along two rays with a
common vertex. Such transforms appear in various mathematical models arising in medical
imaging, nuclear industry and homeland security. This paper contains new results about
inversion of conical Radon transform with fixed opening angle and vertical central axis in …
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In it maps a function to its surface integrals over circular cones, and in it maps a function to its integrals along two rays with a common vertex. Such transforms appear in various mathematical models arising in medical imaging, nuclear industry and homeland security. This paper contains new results about inversion of conical Radon transform with fixed opening angle and vertical central axis in and . New simple explicit inversion formulae are presented in these cases. Numerical simulations were performed to demonstrate the efficiency of the suggested algorithm in 2D.
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