A generalization of a classical discrete tomography problem is considered: reconstruct three-dimensional lattice sets from their two-dimensional X-rays parallel to three coordinate planes. First, we prove that this reconstruction problem is NP-hard. Then we propose some greedy algorithms that provide approximate solutions of the problem.
Brunetti, S., DEL LUNGO, A., Gerard, Y. (2001). On the computational complexity of determining three dimensional lattice sets from their three dimensional X-rays. LINEAR ALGEBRA AND ITS APPLICATIONS, 339(1-3), 59-73 [10.1016/S0024-3795(01)00437-2].
On the computational complexity of determining three dimensional lattice sets from their three dimensional X-rays
BRUNETTI S.;
2001-01-01
Abstract
A generalization of a classical discrete tomography problem is considered: reconstruct three-dimensional lattice sets from their two-dimensional X-rays parallel to three coordinate planes. First, we prove that this reconstruction problem is NP-hard. Then we propose some greedy algorithms that provide approximate solutions of the problem.
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https://hdl.handle.net/11365/12357
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